Master File
Joanna Duran, Nikhil Gupta, Max Moro
2019-03-15 15:05:43
User Inputs
output.var = params$output.var
transform.abs = FALSE
log.pred = params$log.pred
norm.pred = FALSE
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 7
## $ output.var : chr "y3"
## $ log.pred : logi TRUE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE# Setup Labels
output.var.tr = if (log.pred == TRUE) paste0(output.var,'.log') else output.var.tr = output.varLoading Data
feat = read.csv('../../Data/features_highprec.csv')
labels = read.csv('../../Data/labels.csv')
predictors = names(dplyr::select(feat,-JobName))
data.ori = inner_join(feat,labels,by='JobName')
#data.ori = inner_join(feat,select_at(labels,c('JobName',output.var)),by='JobName')Data validation
cc = complete.cases(data.ori)
data.notComplete = data.ori[! cc,]
data = data.ori[cc,] %>% select_at(c(predictors,output.var,'JobName'))
message('Original cases: ',nrow(data.ori))## Original cases: 10000message('Non-Complete cases: ',nrow(data.notComplete))## Non-Complete cases: 3020message('Complete cases: ',nrow(data))## Complete cases: 6980summary(dplyr::select_at(data,c('JobName',output.var)))## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.29
## Job_00003: 1 Median :124.03
## Job_00004: 1 Mean :125.40
## Job_00007: 1 3rd Qu.:131.06
## Job_00008: 1 Max. :193.73
## (Other) :6974Output Variable
The Output Variable y3 shows right skewness, so will proceed with a log transformation
Histogram
df=gather(select_at(data,output.var))
ggplot(df, aes(x=value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() 
#stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value))) QQPlot
ggplot(gather(select_at(data,output.var)), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Trasformation of Output Variable from y3 to y3.log
if(log.pred==TRUE) data[[output.var.tr]] = log(data[[output.var]],10) else
data[[output.var.tr]] = data[[output.var]]
df=gather(select_at(data,c(output.var,output.var.tr)))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=2)
ggplot(gather(select_at(data,c(output.var,output.var.tr))), aes(sample=value)) +
stat_qq() +
facet_wrap(~key, scales = 'free',ncol=4)
Best Normalizator y3
Normalization of y3 using bestNormalize package. (suggested orderNorm) This is cool, but I think is too far for the objective of the project
t=bestNormalize::bestNormalize(data[[output.var]])t## Best Normalizing transformation with 6980 Observations
## Estimated Normality Statistics (Pearson P / df, lower => more normal):
## - No transform: 2.9491
## - Box-Cox: 1.4149
## - Log_b(x+a): 1.9707
## - sqrt(x+a): 2.385
## - exp(x): 749.5512
## - arcsinh(x): 1.9705
## - Yeo-Johnson: 1.1284
## - orderNorm: 1.0815
## Estimation method: Out-of-sample via CV with 10 folds and 5 repeats
##
## Based off these, bestNormalize chose:
## orderNorm Transformation with 6980 nonmissing obs and no ties
## - Original quantiles:
## 0% 25% 50% 75% 100%
## 95.913 118.289 124.030 131.059 193.726qqnorm(data[[output.var]])
qqnorm(predict(t))
orderNorm() is a rank-based procedure by which the values of a vector are mapped to their percentile, which is then mapped to the same percentile of the normal distribution. Without the presence of ties, this essentially guarantees that the transformation leads to a uniform distribution
Predictors
All predictors show a Fat-Tail situation, where the two tails are very tall, and a low distribution around the mean. The orderNorm transformation can help (see [Best Normalizator] section)
Interesting Predictors
Histograms
cols = c('x11','x18','stat98','x7','stat110')
df=gather(select_at(data,cols))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=3)
# ggplot(gather(select_at(data,cols)), aes(sample=value)) +
# stat_qq()+
# facet_wrap(~key, scales = 'free',ncol=2)
lapply(select_at(data,cols),summary)## $x11
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 9.000e-08 9.494e-08 1.001e-07 1.001e-07 1.052e-07 1.100e-07
##
## $x18
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.500 3.147 4.769 4.772 6.418 7.999
##
## $stat98
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.998619 -1.551882 -0.015993 -0.005946 1.528405 2.999499
##
## $x7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.700 1.266 1.854 1.852 2.446 3.000
##
## $stat110
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -2.999543 -1.496865 -0.002193 -0.004129 1.504273 2.999563Scatter plot vs. output variable **y3.log
d = gather(dplyr::select_at(data,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light green',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=3)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
All Predictors
Histograms
All indicators have a strong indication of Fat-Tails
df=gather(select_at(data,predictors))
ggplot(df, aes(value)) +
geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
geom_density() +
# stat_function(fun = dnorm, n = 100, args = list(mean = mean(df$value), sd = sd(df$value)))
facet_wrap(~key, scales = 'free',ncol=4)
Correlations
With Output Variable
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of(output.var.tr,'JobName'))
,select_at(data,output.var.tr)),4)) %>%
rownames_to_column(var='variable') %>% filter(variable != !!output.var) %>% arrange(-y3.log)
#DT::datatable(t)
message("Top Positive")## Top Positivekable(head(arrange(t,desc(y3.log)),20))| variable | y3.log |
|---|---|
| x18 | 0.3120 |
| x7 | 0.2091 |
| stat98 | 0.1784 |
| x9 | 0.1127 |
| x17 | 0.0611 |
| x16 | 0.0489 |
| x10 | 0.0472 |
| x21 | 0.0412 |
| x11 | 0.0322 |
| x8 | 0.0318 |
| stat156 | 0.0287 |
| stat23 | 0.0234 |
| stat100 | 0.0206 |
| stat144 | 0.0203 |
| stat59 | 0.0202 |
| stat60 | 0.0199 |
| stat195 | 0.0199 |
| stat141 | 0.0194 |
| stat73 | 0.0192 |
| stat197 | 0.0185 |
message("Top Negative")## Top Negativekable(head(arrange(t,y3.log),20))| variable | y3.log |
|---|---|
| stat110 | -0.1594 |
| x4 | -0.0603 |
| stat13 | -0.0345 |
| stat41 | -0.0345 |
| stat14 | -0.0317 |
| stat149 | -0.0309 |
| stat113 | -0.0279 |
| stat4 | -0.0248 |
| stat106 | -0.0236 |
| stat146 | -0.0236 |
| stat186 | -0.0217 |
| stat91 | -0.0210 |
| stat214 | -0.0209 |
| stat5 | -0.0207 |
| stat22 | -0.0202 |
| stat39 | -0.0202 |
| stat175 | -0.0194 |
| stat187 | -0.0193 |
| stat128 | -0.0192 |
| stat37 | -0.0191 |
Between All Variables
#chart.Correlation(select(data,-JobName), pch=21)
t=as.data.frame(round(cor(dplyr::select(data,-one_of('JobName'))),4))
#DT::datatable(t,options=list(scrollX=T))
message("Showing only 10 variables")## Showing only 10 variableskable(t[1:10,1:10])| x1 | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| x1 | 1.0000 | 0.0034 | -0.0028 | 0.0085 | 0.0068 | 0.0159 | 0.0264 | -0.0012 | 0.0142 | 0.0013 |
| x2 | 0.0034 | 1.0000 | -0.0057 | 0.0004 | -0.0094 | -0.0101 | 0.0089 | 0.0078 | 0.0049 | -0.0214 |
| x3 | -0.0028 | -0.0057 | 1.0000 | 0.0029 | 0.0046 | 0.0006 | -0.0105 | -0.0002 | 0.0167 | -0.0137 |
| x4 | 0.0085 | 0.0004 | 0.0029 | 1.0000 | -0.0059 | 0.0104 | 0.0098 | 0.0053 | 0.0061 | -0.0023 |
| x5 | 0.0068 | -0.0094 | 0.0046 | -0.0059 | 1.0000 | 0.0016 | -0.0027 | 0.0081 | 0.0259 | -0.0081 |
| x6 | 0.0159 | -0.0101 | 0.0006 | 0.0104 | 0.0016 | 1.0000 | 0.0200 | -0.0157 | 0.0117 | -0.0072 |
| x7 | 0.0264 | 0.0089 | -0.0105 | 0.0098 | -0.0027 | 0.0200 | 1.0000 | -0.0018 | -0.0069 | -0.0221 |
| x8 | -0.0012 | 0.0078 | -0.0002 | 0.0053 | 0.0081 | -0.0157 | -0.0018 | 1.0000 | 0.0142 | -0.0004 |
| x9 | 0.0142 | 0.0049 | 0.0167 | 0.0061 | 0.0259 | 0.0117 | -0.0069 | 0.0142 | 1.0000 | 0.0149 |
| x10 | 0.0013 | -0.0214 | -0.0137 | -0.0023 | -0.0081 | -0.0072 | -0.0221 | -0.0004 | 0.0149 | 1.0000 |
Scatter Plots with Output Variable
Scatter plots with all predictors and the output variable (y3.log)
d = gather(dplyr::select_at(data,c(predictors,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Multicollinearity - VIF
No Multicollinearity among predictors
Showing Top predictor by VIF Value
vifDF = usdm::vif(select_at(data,predictors)) %>% arrange(desc(VIF))
head(vifDF,15)## Variables VIF
## 1 stat145 1.063704
## 2 stat142 1.062756
## 3 stat154 1.061976
## 4 stat1 1.059943
## 5 stat5 1.059813
## 6 stat93 1.059749
## 7 stat32 1.059513
## 8 stat156 1.059133
## 9 stat86 1.058644
## 10 stat14 1.058343
## 11 stat92 1.058224
## 12 stat150 1.058180
## 13 stat127 1.058168
## 14 stat200 1.058121
## 15 stat131 1.058006Feature Eng
- Square Root transformation for x18
data.tr=data %>%
mutate(x18.sqrt = sqrt(x18))
cols=c('x18','x18.sqrt')Comparing Pre and Post Transformation Density Plots
# ggplot(gather(select_at(data.tr,cols)), aes(value)) +
# geom_histogram(aes(y=..density..),bins = 50,fill='light blue') +
# geom_density() +
# facet_wrap(~key, scales = 'free',ncol=4)
d = gather(dplyr::select_at(data.tr,c(cols,output.var.tr)),key=target,value=value,-!!output.var.tr)
ggplot(data=d, aes_string(x='value',y=output.var.tr)) +
geom_point(color='light blue',alpha=0.5) +
geom_smooth() +
facet_wrap(~target, scales = 'free',ncol=4)## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
#removing unwanted variables
data.tr=data.tr %>%
dplyr::select_at(names(data.tr)[! names(data.tr) %in% c('x18','y3','JobName')])
data=data.tr
label.names=output.var.trModeling
PCA
data = data[sample(nrow(data)),] # randomly shuffle data
pca.vars = names(data)
pca.vars = pca.vars[!pca.vars %in% label.names]
#pca.model = preProcess(data[,pca.vars], method = "pca")
#data.pca = predict(pca.model,data)
#eigenVectors = pca.model$rotation
targetCumVar = .8
pca.model = prcomp(data[,pca.vars],center=T,scale.=T,retx = T)
pca.model$var = pca.model$sdev ^ 2 #eigenvalues
pca.model$pvar = pca.model$var / sum(pca.model$var)
pca.model$cumpvar = cumsum(pca.model$pvar )
pca.model$pcaSel = pca.model$cumpvar<=targetCumVar
pca.model$pcaSelCount = sum(pca.model$pcaSel)
pca.model$pcaSelTotVar = sum(pca.model$pvar[pca.model$pcaSel])
message(pca.model$pcaSelCount, " PCAs justify ",percent(targetCumVar)," of the total Variance. (",percent(pca.model$pcaSelTotVar),")")## 177 PCAs justify 80.0% of the total Variance. (79.7%)plot(pca.model$var,xlab="Principal component", ylab="Proportion of variance explained", type='b')
plot(cumsum(pca.model$pvar ),xlab="Principal component", ylab="Cumulative Proportion of variance explained", ylim=c(0,1), type='b')
screeplot(pca.model,npcs = pca.model$pcaSelCount)
screeplot(pca.model,npcs = pca.model$pcaSelCount,type='lines')
summary(pca.model)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9 PC10 PC11 PC12
## Standard deviation 1.17904 1.17584 1.17362 1.17015 1.16717 1.16347 1.15866 1.15734 1.15524 1.15379 1.15158 1.15032
## Proportion of Variance 0.00579 0.00576 0.00574 0.00571 0.00568 0.00564 0.00559 0.00558 0.00556 0.00555 0.00553 0.00551
## Cumulative Proportion 0.00579 0.01155 0.01729 0.02300 0.02867 0.03431 0.03991 0.04549 0.05105 0.05660 0.06212 0.06764
## PC13 PC14 PC15 PC16 PC17 PC18 PC19 PC20 PC21 PC22 PC23 PC24
## Standard deviation 1.14783 1.14539 1.14484 1.14203 1.14161 1.14078 1.13593 1.13406 1.13153 1.12860 1.1273 1.12574
## Proportion of Variance 0.00549 0.00547 0.00546 0.00543 0.00543 0.00542 0.00538 0.00536 0.00533 0.00531 0.0053 0.00528
## Cumulative Proportion 0.07312 0.07859 0.08405 0.08949 0.09492 0.10034 0.10572 0.11107 0.11641 0.12172 0.1270 0.13229
## PC25 PC26 PC27 PC28 PC29 PC30 PC31 PC32 PC33 PC34 PC35 PC36
## Standard deviation 1.12538 1.12293 1.12249 1.11902 1.11784 1.1171 1.11463 1.11240 1.11114 1.10898 1.10838 1.10540
## Proportion of Variance 0.00528 0.00525 0.00525 0.00522 0.00521 0.0052 0.00518 0.00516 0.00514 0.00512 0.00512 0.00509
## Cumulative Proportion 0.13757 0.14282 0.14807 0.15329 0.15850 0.1637 0.16887 0.17403 0.17917 0.18430 0.18942 0.19451
## PC37 PC38 PC39 PC40 PC41 PC42 PC43 PC44 PC45 PC46 PC47 PC48
## Standard deviation 1.10363 1.10119 1.09868 1.09712 1.09664 1.0953 1.09342 1.09248 1.09191 1.08993 1.08755 1.08740
## Proportion of Variance 0.00508 0.00505 0.00503 0.00502 0.00501 0.0050 0.00498 0.00497 0.00497 0.00495 0.00493 0.00493
## Cumulative Proportion 0.19958 0.20464 0.20967 0.21468 0.21969 0.2247 0.22967 0.23465 0.23961 0.24456 0.24949 0.25442
## PC49 PC50 PC51 PC52 PC53 PC54 PC55 PC56 PC57 PC58 PC59 PC60
## Standard deviation 1.0848 1.0839 1.08256 1.07975 1.07796 1.07724 1.07681 1.07518 1.0738 1.0732 1.07179 1.06978
## Proportion of Variance 0.0049 0.0049 0.00488 0.00486 0.00484 0.00484 0.00483 0.00482 0.0048 0.0048 0.00479 0.00477
## Cumulative Proportion 0.2593 0.2642 0.26910 0.27396 0.27880 0.28363 0.28847 0.29328 0.2981 0.3029 0.30767 0.31244
## PC61 PC62 PC63 PC64 PC65 PC66 PC67 PC68 PC69 PC70 PC71 PC72
## Standard deviation 1.06760 1.06694 1.06668 1.06530 1.06432 1.06296 1.06035 1.05938 1.05854 1.05756 1.05511 1.05364
## Proportion of Variance 0.00475 0.00474 0.00474 0.00473 0.00472 0.00471 0.00468 0.00468 0.00467 0.00466 0.00464 0.00463
## Cumulative Proportion 0.31719 0.32193 0.32667 0.33140 0.33612 0.34083 0.34551 0.35019 0.35486 0.35952 0.36416 0.36878
## PC73 PC74 PC75 PC76 PC77 PC78 PC79 PC80 PC81 PC82 PC83 PC84
## Standard deviation 1.05283 1.05150 1.0504 1.04991 1.04971 1.04759 1.04638 1.04417 1.04337 1.04268 1.04064 1.04021
## Proportion of Variance 0.00462 0.00461 0.0046 0.00459 0.00459 0.00457 0.00456 0.00454 0.00454 0.00453 0.00451 0.00451
## Cumulative Proportion 0.37340 0.37801 0.3826 0.38720 0.39179 0.39636 0.40092 0.40547 0.41000 0.41453 0.41905 0.42355
## PC85 PC86 PC87 PC88 PC89 PC90 PC91 PC92 PC93 PC94 PC95 PC96
## Standard deviation 1.0387 1.03784 1.03567 1.03512 1.03323 1.03261 1.03067 1.03016 1.02847 1.02686 1.02606 1.02388
## Proportion of Variance 0.0045 0.00449 0.00447 0.00446 0.00445 0.00444 0.00443 0.00442 0.00441 0.00439 0.00439 0.00437
## Cumulative Proportion 0.4280 0.43254 0.43701 0.44147 0.44592 0.45036 0.45479 0.45921 0.46362 0.46801 0.47240 0.47677
## PC97 PC98 PC99 PC100 PC101 PC102 PC103 PC104 PC105 PC106 PC107 PC108
## Standard deviation 1.02321 1.02236 1.02153 1.02046 1.01984 1.01900 1.01740 1.01448 1.01392 1.01179 1.01081 1.00838
## Proportion of Variance 0.00436 0.00436 0.00435 0.00434 0.00433 0.00433 0.00431 0.00429 0.00428 0.00427 0.00426 0.00424
## Cumulative Proportion 0.48113 0.48548 0.48983 0.49417 0.49850 0.50283 0.50714 0.51143 0.51572 0.51998 0.52424 0.52847
## PC109 PC110 PC111 PC112 PC113 PC114 PC115 PC116 PC117 PC118 PC119 PC120
## Standard deviation 1.00788 1.00643 1.00572 1.00466 1.00314 1.00249 1.00058 0.99679 0.99672 0.99594 0.99554 0.99487
## Proportion of Variance 0.00423 0.00422 0.00421 0.00421 0.00419 0.00419 0.00417 0.00414 0.00414 0.00413 0.00413 0.00412
## Cumulative Proportion 0.53271 0.53693 0.54114 0.54535 0.54954 0.55373 0.55790 0.56204 0.56618 0.57031 0.57444 0.57857
## PC121 PC122 PC123 PC124 PC125 PC126 PC127 PC128 PC129 PC130 PC131 PC132
## Standard deviation 0.99314 0.99094 0.99017 0.98931 0.98824 0.98724 0.98619 0.98451 0.98265 0.98147 0.98058 0.9795
## Proportion of Variance 0.00411 0.00409 0.00409 0.00408 0.00407 0.00406 0.00405 0.00404 0.00402 0.00401 0.00401 0.0040
## Cumulative Proportion 0.58268 0.58677 0.59085 0.59493 0.59900 0.60306 0.60711 0.61115 0.61517 0.61919 0.62319 0.6272
## PC133 PC134 PC135 PC136 PC137 PC138 PC139 PC140 PC141 PC142 PC143 PC144
## Standard deviation 0.97894 0.97768 0.97560 0.97556 0.97296 0.97076 0.96990 0.96870 0.96836 0.96667 0.96534 0.96506
## Proportion of Variance 0.00399 0.00398 0.00397 0.00397 0.00394 0.00393 0.00392 0.00391 0.00391 0.00389 0.00388 0.00388
## Cumulative Proportion 0.63118 0.63517 0.63913 0.64310 0.64704 0.65097 0.65489 0.65880 0.66271 0.66660 0.67048 0.67436
## PC145 PC146 PC147 PC148 PC149 PC150 PC151 PC152 PC153 PC154 PC155 PC156
## Standard deviation 0.96324 0.96255 0.96210 0.96047 0.95901 0.95753 0.95677 0.95569 0.95395 0.95280 0.95148 0.94924
## Proportion of Variance 0.00387 0.00386 0.00386 0.00384 0.00383 0.00382 0.00381 0.00381 0.00379 0.00378 0.00377 0.00375
## Cumulative Proportion 0.67823 0.68209 0.68595 0.68979 0.69362 0.69744 0.70126 0.70506 0.70885 0.71264 0.71641 0.72016
## PC157 PC158 PC159 PC160 PC161 PC162 PC163 PC164 PC165 PC166 PC167 PC168
## Standard deviation 0.94857 0.94819 0.94749 0.94599 0.94465 0.94380 0.94369 0.9418 0.94114 0.93935 0.93790 0.93584
## Proportion of Variance 0.00375 0.00375 0.00374 0.00373 0.00372 0.00371 0.00371 0.0037 0.00369 0.00368 0.00367 0.00365
## Cumulative Proportion 0.72391 0.72766 0.73140 0.73513 0.73885 0.74256 0.74627 0.7500 0.75365 0.75733 0.76100 0.76465
## PC169 PC170 PC171 PC172 PC173 PC174 PC175 PC176 PC177 PC178 PC179 PC180
## Standard deviation 0.93500 0.93343 0.93208 0.93200 0.9300 0.9295 0.92698 0.92643 0.92505 0.92385 0.92325 0.92122
## Proportion of Variance 0.00364 0.00363 0.00362 0.00362 0.0036 0.0036 0.00358 0.00358 0.00357 0.00356 0.00355 0.00354
## Cumulative Proportion 0.76829 0.77192 0.77554 0.77916 0.7828 0.7864 0.78994 0.79352 0.79708 0.80064 0.80419 0.80773
## PC181 PC182 PC183 PC184 PC185 PC186 PC187 PC188 PC189 PC190 PC191 PC192
## Standard deviation 0.91894 0.91786 0.9165 0.9160 0.91558 0.91396 0.91183 0.90944 0.90827 0.90721 0.90632 0.90529
## Proportion of Variance 0.00352 0.00351 0.0035 0.0035 0.00349 0.00348 0.00346 0.00345 0.00344 0.00343 0.00342 0.00341
## Cumulative Proportion 0.81125 0.81476 0.8183 0.8217 0.82525 0.82873 0.83219 0.83564 0.83907 0.84250 0.84593 0.84934
## PC193 PC194 PC195 PC196 PC197 PC198 PC199 PC200 PC201 PC202 PC203 PC204
## Standard deviation 0.90457 0.9034 0.90208 0.90105 0.89916 0.89772 0.89656 0.89605 0.89191 0.89167 0.8906 0.88912
## Proportion of Variance 0.00341 0.0034 0.00339 0.00338 0.00337 0.00336 0.00335 0.00335 0.00331 0.00331 0.0033 0.00329
## Cumulative Proportion 0.85275 0.8561 0.85954 0.86292 0.86629 0.86965 0.87300 0.87635 0.87966 0.88297 0.8863 0.88957
## PC205 PC206 PC207 PC208 PC209 PC210 PC211 PC212 PC213 PC214 PC215 PC216
## Standard deviation 0.88740 0.88429 0.88386 0.88233 0.88045 0.87944 0.87867 0.87734 0.8757 0.87283 0.87119 0.86998
## Proportion of Variance 0.00328 0.00326 0.00326 0.00324 0.00323 0.00322 0.00322 0.00321 0.0032 0.00317 0.00316 0.00315
## Cumulative Proportion 0.89285 0.89611 0.89937 0.90261 0.90584 0.90906 0.91228 0.91549 0.9187 0.92186 0.92502 0.92817
## PC217 PC218 PC219 PC220 PC221 PC222 PC223 PC224 PC225 PC226 PC227 PC228
## Standard deviation 0.86891 0.86819 0.86572 0.86341 0.8623 0.85963 0.85747 0.85597 0.85552 0.85423 0.85298 0.85038
## Proportion of Variance 0.00315 0.00314 0.00312 0.00311 0.0031 0.00308 0.00306 0.00305 0.00305 0.00304 0.00303 0.00301
## Cumulative Proportion 0.93132 0.93446 0.93758 0.94069 0.9438 0.94686 0.94993 0.95298 0.95603 0.95907 0.96210 0.96512
## PC229 PC230 PC231 PC232 PC233 PC234 PC235 PC236 PC237 PC238 PC239 PC240
## Standard deviation 0.84687 0.84630 0.84533 0.84209 0.84002 0.83569 0.8336 0.83335 0.82944 0.82661 0.82391 0.8197
## Proportion of Variance 0.00299 0.00298 0.00298 0.00295 0.00294 0.00291 0.0029 0.00289 0.00287 0.00285 0.00283 0.0028
## Cumulative Proportion 0.96810 0.97109 0.97407 0.97702 0.97996 0.98287 0.9858 0.98866 0.99153 0.99437 0.99720 1.0000pca.model$rotation## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## x1 0.0767879107 -0.0217177036 0.0788201126 -0.0808250934 0.1504043126 -0.0279115015 0.1007238424
## x2 0.1006911186 -0.0912806138 0.0238059802 0.0045564663 -0.0422689744 -0.0187605595 0.0145961545
## x3 0.0371213351 -0.0494977004 0.0892244600 -0.0701034222 -0.0168940876 0.0143530305 -0.0835037931
## x4 0.0134238521 0.0414990175 -0.0311865424 0.0145658214 0.0610881472 -0.0025793875 0.0946469940
## x5 0.0749073012 -0.0422571907 -0.0715208061 -0.0318403437 0.0020384488 0.0385535191 -0.0593562724
## x6 0.1684389241 -0.1019150393 -0.0536506485 0.1223885886 -0.0213455035 -0.0830749680 0.0941929548
## x7 0.1262484390 -0.0590049476 -0.0317433065 -0.0305791954 -0.0284526763 -0.0003559020 0.0530059512
## x8 0.0899359345 0.0536865753 -0.0449581122 0.1252133593 0.0742279666 0.0437725290 -0.0864538398
## x9 0.0459976808 -0.0076731002 0.0964902116 0.0295167711 0.0335766244 -0.0634732737 0.0042358579
## x10 0.0088379822 0.0104602995 0.0301179407 -0.0635642121 0.0512863036 0.0137180117 0.0184930977
## x11 -0.0261786136 0.0810057228 -0.0266485066 -0.0436429993 -0.0240474030 0.0518417495 0.1145906623
## x12 0.0218857155 -0.0634142440 -0.1255972630 -0.0097015127 0.0254327417 -0.0161530952 0.0231278192
## x13 0.1201588396 0.0538641732 0.0357342946 -0.0123800820 -0.0647222459 -0.0447698072 -0.0629430712
## x14 -0.0756219648 -0.0163225317 -0.1209003903 -0.0657399610 0.0346005119 0.0442172597 0.1019755222
## x15 0.1076821399 0.0299032069 -0.0337952844 -0.0380445639 -0.0084948416 0.0425967485 -0.1032656178
## x16 0.0113137679 -0.0274374274 0.0127301778 0.0195100479 0.0294842293 0.0664049484 -0.0055785857
## x17 -0.0267906643 0.0569964759 -0.0715791427 0.1281743275 -0.1035395353 -0.0888648245 0.1018815039
## x19 0.0319076124 -0.0719988194 0.1168537650 0.0438754832 0.0004223923 -0.0262353173 0.0771117440
## x20 -0.1111175408 -0.0315224660 0.0466966918 -0.0356713473 -0.0400249048 0.0254261914 -0.0156458583
## x21 -0.0379417717 -0.0062248415 -0.0561242495 -0.1016645223 -0.0199752678 0.0281449592 0.0459741647
## x22 0.0901163392 0.0468290081 -0.1713145665 0.0511751203 -0.0705052814 -0.0897118796 -0.0911410246
## x23 0.0186288219 0.0277115504 0.0356372620 -0.0800338353 -0.0012887515 0.0624076101 -0.1066800084
## stat1 0.0662232976 -0.0605751173 -0.0237021445 -0.0837486956 0.1295326751 0.1233993849 0.0038906821
## stat2 0.1854658767 0.0222427882 0.0302007982 0.0339168877 -0.0568638552 0.1015553326 -0.0116363347
## stat3 0.0196157164 0.0397928576 0.0462238515 0.0455611126 -0.1078755057 0.0490303150 -0.0689181234
## stat4 -0.1431349938 0.0803432697 -0.0501863777 -0.0322929143 -0.0522333595 -0.0614230671 -0.0292554875
## stat5 0.0330391164 0.1115025825 -0.0805648949 -0.1055216315 -0.0358140622 0.0596512630 -0.0210614802
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## stat8 0.0177159794 -0.0834860312 0.0603181339 0.0115933639 0.0192834208 -0.0107711161 0.0053836244
## stat9 0.0214186773 0.0719209968 0.0487617902 0.0233774844 0.1163507343 0.0964858892 0.0702832556
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## stat12 0.0499709358 0.0975800825 0.1303586783 0.0021395303 -0.0732534084 -0.1040796466 -0.0080442287
## stat13 -0.1281745644 -0.0648097272 -0.0456352081 0.0036465936 0.0602639881 -0.0380276625 -0.0287454913
## stat14 0.1684241312 -0.1078838376 0.0586995170 0.0199803789 0.1119769840 -0.0516568179 -0.0047519101
## stat15 -0.0191846066 0.0092712232 -0.0400425375 -0.1599130970 0.0252962043 0.0930514327 0.0340474186
## stat16 -0.0506536102 -0.0631828015 -0.0037002074 0.0236011115 -0.0696534779 0.0010557752 -0.0398968779
## stat17 -0.0858265895 0.0400681955 0.0806657311 -0.1774349148 -0.0229559369 0.0456616287 0.1620883904
## stat18 0.0425597491 -0.0474965563 0.1225798316 -0.0870817245 -0.0015020908 -0.0251126634 0.0249970943
## stat19 -0.1382107042 -0.0250080004 -0.0429261762 -0.0809903710 0.1330807802 0.0041749056 0.0570832337
## stat20 0.0208942849 0.0045286295 -0.0981006835 -0.0472885845 0.0926127836 0.1023906641 -0.0391156938
## stat21 -0.0189482396 0.0167723862 0.0231155546 0.0056406784 0.0565566255 0.0160471366 0.0269969077
## stat22 0.0266959448 -0.0576118332 0.0244111802 -0.0715555672 0.0086410733 -0.0522751808 -0.0027746051
## stat23 0.0314351226 -0.0677009407 0.0666788171 -0.0288889285 0.0716847832 0.0500080924 -0.0272393711
## stat24 -0.0249176576 0.0723459281 -0.0161341740 -0.0299242424 0.0018290495 0.0582487235 -0.0128087436
## stat25 0.0864983234 0.0326474852 -0.0496841901 0.0030073267 -0.0326974368 0.0589363714 0.0356771050
## stat26 0.0505984455 -0.0389291708 -0.0110295519 0.0175450320 -0.0562745413 -0.1295966758 0.0053648746
## stat27 -0.0367143850 -0.0794395320 -0.0039099244 0.0006124688 -0.0822422331 0.0530407423 0.0213901943
## stat28 0.0526646946 -0.0428017055 -0.0570925145 -0.0072249921 -0.0554435437 -0.0140654441 -0.0077797091
## stat29 0.0374922105 -0.0475866800 0.0791463064 0.0603486998 -0.0290655833 -0.0228338623 0.0092377081
## stat30 0.0822437735 0.0532236472 -0.1330988779 0.0005684349 0.0948571841 -0.0169632202 -0.0110818963
## stat31 0.1754056198 0.0884828662 0.0671092511 -0.0012718301 -0.0181112963 -0.0912588183 0.0596420306
## stat32 -0.0419118311 0.0720057198 0.0116205234 -0.0816917104 -0.0513415869 0.0510279445 -0.0112933925
## stat33 -0.0989245479 0.0180958835 0.0021880680 -0.0054893777 0.0018353371 0.1353975172 -0.0473448610
## stat34 -0.0565932728 -0.0585592254 -0.0565931015 0.0854042774 -0.0779211414 0.0372014830 0.0251317480
## stat35 -0.0381996911 -0.0504572124 -0.0415067609 0.0137697330 -0.0789381937 0.0315999347 0.1044369602
## stat36 -0.0111426521 -0.0204649006 0.0672130542 -0.0243048036 0.0257929459 0.0222927667 0.0263346551
## stat37 0.0980860305 -0.0478856727 0.1424926970 -0.1056410440 -0.0306330541 -0.0323766955 -0.1588729903
## stat38 -0.0479602629 -0.0106542629 0.0010985797 -0.1123698330 -0.0074310077 -0.0269908047 0.0872662493
## stat39 -0.0730431154 0.0718262329 -0.0076191957 0.0081747468 -0.0575864903 -0.0347867271 -0.0056733847
## stat40 0.0149684130 -0.0296842504 -0.0317468078 -0.0653024982 0.0189452516 0.0637704541 0.1207913123
## stat41 0.0702934699 0.0896120558 -0.0596440750 -0.0078865782 -0.0264422736 -0.0479419313 0.0215072776
## stat42 0.0940531171 0.0052112484 0.0363021065 -0.0076444976 -0.0418917059 0.0089501350 0.1085411228
## stat43 -0.0305707274 0.1163733680 -0.0753325465 -0.0661547818 0.0068631116 0.0226891351 -0.0204990266
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## stat46 0.0698980157 -0.0167727758 -0.1574297632 0.0172883381 -0.0759403136 0.0153227335 -0.0373706246
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## PC8 PC9 PC10 PC11 PC12 PC13 PC14
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## PC22 PC23 PC24 PC25 PC26 PC27 PC28 PC29
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## PC30 PC31 PC32 PC33 PC34 PC35 PC36 PC37
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## PC38 PC39 PC40 PC41 PC42 PC43 PC44 PC45
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## PC54 PC55 PC56 PC57 PC58 PC59 PC60 PC61
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## x2 0.1058759806 0.069815167 0.0383028011 -0.0558569706 -0.0294847785 -0.0663388554 0.1211537616 -0.0238609365
## x3 -0.0718661958 -0.001187508 -0.0108167834 -0.0859038109 0.0471944783 0.1615687263 0.0040965640 -0.0231336362
## x4 -0.0658862355 0.002141611 0.0584418876 0.0303261864 0.0340750356 -0.0399354290 0.0282157554 -0.0957091014
## x5 0.0913316928 0.006977725 0.1184609797 -0.0007836062 0.1307669055 -0.0146375309 0.0534145124 0.0625673597
## x6 0.0851561357 0.014171626 -0.0790863248 0.0886927949 -0.0278777481 0.0340830015 -0.0603237736 -0.0989741299
## x7 -0.0633192466 0.118359095 -0.1064557570 0.0356161868 0.0594056279 -0.0523721395 -0.0502372923 0.0048868987
## x8 -0.1557034608 0.016762108 -0.0768647293 0.0424308740 0.1910226604 -0.0779341375 0.0145359517 0.0170408570
## x9 0.0192762205 -0.050412181 0.0323024757 0.0685581168 0.0166600206 -0.0476305964 0.0091130651 0.0010709477
## x10 -0.0585746755 -0.046441531 -0.0588591176 0.0142237025 0.0106788090 0.0160384619 -0.1097922234 0.0348852392
## x11 -0.0318879133 -0.095021463 -0.0294180275 -0.1524469294 0.0155201031 0.0317283863 0.0470901639 -0.1237507827
## x12 -0.0109065263 -0.024861349 0.0579963494 -0.0878691159 0.0272472238 -0.0235064826 -0.0074211016 -0.0297963073
## x13 0.0087762417 -0.003623910 -0.0124875555 0.0115462419 -0.0121658550 0.0466444679 0.0614662514 0.0363093440
## x14 -0.0071490451 -0.008171736 -0.0100001643 -0.0570777390 0.0026486828 -0.0327973568 -0.0066693433 -0.0468791810
## x15 -0.0500109906 0.010250359 0.0525062069 -0.0495075792 0.0850842407 -0.0689498637 0.0816714504 0.0526509933
## x16 0.1033121478 -0.070917415 0.1645440464 -0.0575071521 -0.0087649928 0.0545924979 0.0358970069 -0.0287199716
## x17 0.0685590494 -0.038604472 0.0421696145 0.0402125199 0.0379734331 -0.1148965419 -0.0072283783 -0.0969030665
## x19 -0.0087496397 -0.032376736 0.1014480967 -0.0562263482 -0.0968269331 0.0094126503 0.0080126327 0.0081604172
## x20 -0.0239389389 0.121702178 0.0750121317 0.0209542587 0.0781805850 -0.0457807841 0.0045472104 0.0780517261
## x21 -0.0361604443 -0.066693619 -0.0046272303 -0.0394601286 0.0201441763 0.0234514351 0.0715244284 -0.0346806706
## x22 0.0406019689 -0.082679569 -0.0215093623 -0.0004851259 -0.0589167804 -0.1019409399 0.0587499431 0.0320548052
## x23 0.0904224096 0.002424696 0.0699909313 0.0236822391 0.1204208681 -0.0150995976 0.0126856847 -0.0333963795
## stat1 0.0106126327 -0.004435257 -0.0337915053 -0.0159767874 0.0066075664 0.0980477524 0.0627014819 -0.0265561119
## stat2 -0.0433345757 0.074347197 0.0296506585 -0.0593089556 0.0464536224 0.0199336188 -0.0052915994 -0.0051957414
## stat3 -0.1293968527 -0.066009826 -0.0445045893 0.0842519167 0.0355297419 -0.0632901524 0.0050103259 0.1241729560
## stat4 0.0756756816 0.014642029 -0.1307220185 0.0853812961 0.0390119419 0.0052345124 0.0351767743 -0.1262599016
## stat5 -0.0574465653 0.039024013 0.0256755330 0.0057293113 -0.1743658457 -0.0266015222 -0.0664864469 0.0517135216
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## stat7 -0.0113894349 0.020428989 0.0361269520 0.0669954389 0.0915536047 0.0874367803 -0.0188849910 -0.1048792343
## stat8 0.0133011795 0.014973756 -0.0269408543 0.0316939492 0.0495582742 -0.0080603650 0.0773139057 0.0154631213
## stat9 0.0263010702 -0.045172265 0.0131555654 -0.0935112317 0.0274052135 0.0023669702 0.0245047443 0.0270292145
## stat10 0.1245829195 -0.013379451 0.0485620390 0.0472335173 0.0732135924 0.0239596102 -0.0947946991 -0.0571922074
## stat11 0.0193615485 -0.035754022 0.0740858242 -0.0217035902 0.1125476663 0.0495950226 0.1340231581 0.0533807365
## stat12 0.0427302896 0.033064734 0.0153196821 -0.0080723148 -0.0913043637 0.0321665034 0.0358907893 -0.0013876205
## stat13 0.0274819997 0.020239780 0.0241812234 0.0005961315 -0.0166576296 0.1136832907 -0.0230738672 0.1081669388
## stat14 -0.0101396083 0.033675907 0.0062911295 0.0105786635 0.0079570240 0.1074652250 0.0140989763 -0.0156881895
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## stat16 0.0169377804 -0.023582581 0.0087753832 -0.0084240892 0.0007939735 -0.0199131446 0.0152680281 -0.0150385543
## stat17 0.0191684017 -0.036095780 -0.0410805393 -0.0343718550 -0.0174539171 -0.0687866249 -0.0174403663 0.0364265428
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## stat20 0.0386076050 0.149257234 -0.0869298711 -0.1519013926 -0.0266476572 -0.1592907579 -0.0235027751 -0.0197475350
## stat21 0.0117584823 -0.028818772 0.0064418960 0.1637387174 0.0470523673 0.0309845207 0.0525481154 0.0472163795
## stat22 0.0322378062 -0.074565958 -0.0708480583 -0.1238859917 -0.0397563893 -0.0005736159 0.1150628052 0.0163405389
## stat23 -0.1178881765 0.076606031 0.0177074190 0.0142705600 0.1079555286 0.0026756791 -0.0109213424 -0.0430700726
## stat24 0.0700100042 0.030677353 0.0150128325 -0.0622703520 0.0060539718 -0.0222411418 0.1467271294 -0.0516026388
## stat25 -0.0081741460 -0.061710791 0.0568515179 -0.0231238677 -0.0090404422 0.0228655375 -0.0882660249 -0.0558854213
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## stat27 0.0037637910 0.041833567 0.0753991274 -0.1031306681 0.0441072880 0.0102504087 -0.0101587600 -0.0121632623
## stat28 0.0263376062 -0.030107212 0.0739722169 -0.1126823758 -0.0131340340 0.0290628773 0.0019745293 -0.0051905908
## stat29 0.0325014671 -0.085820383 -0.0039484852 0.0955548516 0.1298807881 -0.0926332606 0.0568465685 0.0037311111
## stat30 0.0272879341 -0.068632501 -0.0537196992 0.1099662088 0.0688685119 0.0671673768 -0.0450289556 0.0449158422
## stat31 0.0119014905 0.035724069 -0.0776161836 0.0077440201 0.0235869522 -0.0054383454 0.1066225027 -0.0169700385
## stat32 0.0360251185 0.048003918 0.0470216082 -0.0291944281 -0.0479009554 -0.0253557106 0.0503507110 0.0780301419
## stat33 0.0570339671 0.026450274 -0.0182013144 0.0637215027 -0.0585138275 -0.0174301723 -0.0083811520 -0.0167440382
## stat34 0.0368508021 -0.079525600 0.0806353617 0.0304390515 0.0107969255 0.0162263501 -0.0278550107 0.0021813130
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## stat38 0.0417299972 0.109894376 0.0562611682 0.1089765060 0.0463515114 0.0797386310 0.0145411974 0.0166548274
## stat39 0.1482331633 0.078185167 -0.0478650261 -0.0916183679 -0.0555286138 0.1043481565 -0.0232824711 -0.0712029956
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## stat41 -0.1471300151 -0.007415161 0.1282119756 0.0215093509 -0.0769798165 -0.1009751610 -0.0647371524 0.1275708123
## stat42 0.0070629313 0.050734366 -0.0425851835 -0.0346206579 0.0243010827 0.0320276350 -0.1375294269 -0.0016312387
## stat43 0.0140111008 0.008313662 0.0460255048 -0.1082433081 0.0697628646 0.0293231829 -0.0693744301 0.0055812590
## stat44 -0.0266252064 -0.007290473 0.0604379154 0.0809342087 0.0383360975 0.0057038600 -0.1044092584 0.0632018005
## stat45 0.0356144835 -0.015542691 0.0668731739 0.0528459322 -0.0404081505 -0.1102125644 0.0385518541 -0.0048456635
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## stat49 0.0363086745 -0.059793495 -0.0242608185 -0.1012518780 -0.0231141156 0.0270959730 0.0144143862 -0.1061324015
## stat50 0.0585145595 0.050886356 -0.1248406758 -0.0281296864 0.1124718910 0.0035833137 -0.0199593772 -0.1187887865
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## stat55 -0.0653500429 0.049061083 0.0870457416 0.0659279840 -0.0528332326 -0.1180542096 -0.0598746324 0.0635052331
## stat56 0.0365251051 -0.070586140 -0.0104701152 -0.0521082216 -0.0186445109 -0.0146048043 0.0301936457 0.0140841664
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## stat58 0.0294976468 0.149626067 -0.0754624073 -0.0169859890 -0.0834192645 0.1195119294 -0.0998721552 0.0090616351
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## PC62 PC63 PC64 PC65 PC66 PC67 PC68 PC69
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## PC100 PC101 PC102 PC103 PC104 PC105 PC106 PC107
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## PC108 PC109 PC110 PC111 PC112 PC113 PC114 PC115
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## PC116 PC117 PC118 PC119 PC120 PC121 PC122
## x1 1.029064e-01 5.138395e-02 3.713336e-02 0.0099745300 0.0467139057 -8.520062e-02 -0.0260430684
## x2 -6.879421e-02 -1.885099e-02 -1.523404e-01 -0.0255948033 0.1050226911 -1.457068e-02 0.0550735055
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## x4 1.373935e-02 2.147495e-02 7.612654e-02 0.0321118158 -0.0198389243 6.981591e-03 0.0404564288
## x5 4.630060e-03 -1.599968e-02 4.868830e-02 -0.1007390289 0.0746038207 1.263024e-01 0.0939180416
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## x7 1.474896e-02 1.294911e-02 -2.020397e-02 0.0086038260 0.0013564238 -3.662154e-02 0.0783900255
## x8 7.926387e-02 9.374039e-03 2.034745e-02 -0.0007295886 0.1394637271 6.243093e-02 0.0964509267
## x9 -5.654704e-02 9.158179e-02 -7.740254e-02 0.0313115291 0.0408149271 -4.627991e-02 0.1007916924
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## x11 2.966573e-02 -9.527732e-02 3.604316e-02 0.0381327025 -0.1034862832 -3.015726e-02 -0.0167843866
## x12 -8.073979e-02 -1.978190e-02 6.945523e-02 0.0103526518 -0.0459484963 6.665177e-02 -0.0228528925
## x13 2.178163e-02 -1.086950e-01 1.001006e-01 0.0493158114 -0.1366857589 9.307102e-02 0.0167928802
## x14 -2.227972e-02 -1.610239e-02 -4.188018e-02 0.0075012288 -0.0464145088 -9.883720e-03 -0.0499661871
## x15 -5.862167e-02 -3.776048e-02 8.628560e-02 -0.0131109649 -0.0057004909 -1.748374e-01 0.0126752385
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## PC130 PC131 PC132 PC133 PC134 PC135 PC136 PC137
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## PC138 PC139 PC140 PC141 PC142 PC143 PC144 PC145
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## x4 7.967910e-03 0.034169436 -0.0620105238 0.0667706529 -0.0064980673 -0.0046930379 0.0399758258 -0.0105181034
## x5 4.970763e-02 -0.009872727 -0.0568277059 0.0269990375 -0.0957969364 -0.1350748544 -0.0124024495 -0.0240938500
## x6 1.359565e-01 0.004854051 0.1528412529 0.1208600466 0.0452355884 0.0625911188 0.0744418002 -0.0361130115
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## x10 1.165054e-01 -0.141745607 -0.0365492609 -0.1118580147 0.1316419238 0.0826675321 0.0109106070 -0.0066881186
## x11 2.593480e-02 -0.063403857 -0.1178925730 0.0260561620 -0.0371131369 -0.0182402544 0.0782325727 0.1118068643
## x12 5.324973e-02 -0.064811711 0.0195859377 -0.0388436979 0.0166548814 0.0217657551 0.0393520801 0.0522692779
## x13 9.000736e-02 0.019219700 -0.0305386201 0.0616000980 0.0014299008 -0.0217554518 0.0708633286 0.0106337301
## x14 1.042657e-01 -0.056564764 0.1207080815 0.0011102722 0.0430985096 0.0907932456 0.0676286208 -0.0727471881
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## stat5 3.010901e-03 -0.064155446 0.0554084979 0.0652135859 0.0007559000 0.0443704581 0.0185016750 -0.0737045509
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## PC182 PC183 PC184 PC185 PC186 PC187 PC188 PC189
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## PC197 PC198 PC199 PC200 PC201 PC202 PC203 PC204
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## x3 4.661583e-02 -3.753161e-03 -0.027876165 0.1019155815 -0.0766303396 0.0335346490 1.000119e-01 9.555967e-03
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## x6 8.316095e-02 -9.479840e-02 -0.029064936 0.0769430013 -0.0297572564 -0.0655589665 -1.674667e-02 7.794049e-03
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## PC205 PC206 PC207 PC208 PC209 PC210 PC211 PC212
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## PC221 PC222 PC223 PC224 PC225 PC226 PC227
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## x8 5.364317e-02 0.0334101455 -0.0180515111 -6.261819e-03 -1.539404e-02 1.034171e-01 -0.0798864946
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## x17 7.645165e-02 0.0665751200 0.0663123066 1.400777e-01 8.320002e-02 4.599634e-02 -0.0277011508
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## stat161 -3.345207e-02 -8.922876e-02 0.0557917993 0.0208148057 -0.1295305722 -0.0365884576
## stat162 -1.383938e-01 9.821353e-02 -0.0728267377 -0.0653782009 -0.0901317995 -0.0239767262
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## stat166 2.016460e-02 -2.489134e-02 -0.0057845085 -0.0038513818 -0.1191387505 -0.0303320913
## stat167 4.509822e-02 5.208747e-02 0.0401245766 0.0771146266 0.0376630621 0.1017527950
## stat168 3.432716e-02 -1.553598e-02 -0.0448131041 0.0518062817 -0.0031598425 -0.0289736918
## stat169 -1.658791e-02 1.894437e-02 -0.0243817308 -0.0738754827 0.1156836581 -0.0076339690
## stat170 7.624686e-02 8.932392e-02 0.0116149023 -0.0107596766 -0.0592266052 -0.0306313900
## stat171 1.306876e-02 -4.271493e-02 0.0824202700 0.1214243267 0.0046300892 0.0104847448
## stat172 4.074941e-02 -1.720226e-02 0.0450076213 -0.0038603663 0.0103578358 0.0077465895
## stat173 -2.520043e-03 -1.169873e-01 0.0389012458 0.0508556194 0.0069197062 0.0958891758
## stat174 -2.054679e-02 -1.108891e-01 -0.0742488962 -0.0676062716 0.0284712272 -0.0158076709
## stat175 6.043142e-02 1.040339e-01 0.1633996383 0.0896956863 -0.0133967586 0.0145783796
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## stat177 -5.915615e-02 -7.931927e-02 -0.0978788625 -0.0302343571 -0.0385699221 0.0379547342
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## stat179 -6.364589e-02 -1.469619e-02 -0.0163024037 0.0821761402 0.0873081628 0.0020827788
## stat180 -7.285344e-02 -4.785916e-02 0.0231369768 0.0905716078 0.0486718793 -0.0973364602
## stat181 -9.326206e-03 -1.359705e-02 0.0564202738 -0.0513861812 -0.0875258095 -0.0045829269
## stat182 4.116711e-02 8.072875e-02 -0.0006763499 0.0054184707 -0.0221971812 0.0709318322
## stat183 -6.198955e-02 -3.343213e-02 -0.0129887888 -0.0175780640 -0.0413373790 -0.0591604083
## stat184 8.618959e-02 1.477174e-02 0.1300526288 -0.0293104367 -0.0140278172 -0.0323005157
## stat185 4.852406e-02 1.462039e-02 -0.0838817157 0.1231453003 0.0649951344 -0.0042900253
## stat186 6.131501e-02 4.416366e-02 0.0503681376 -0.0207197312 -0.0267203540 0.0295689864
## stat187 9.143951e-02 3.618453e-03 -0.0327471799 0.0510990459 -0.1476633055 0.0105507161
## stat188 -7.027411e-02 -7.858488e-02 0.0225649700 -0.0183504203 -0.0204333019 0.1399812631
## stat189 7.762811e-02 4.131593e-02 0.0359128981 0.0751023135 0.0407133918 0.1536420739
## stat190 1.935077e-02 -6.258625e-02 -0.0800133465 0.1281728840 0.0573211464 -0.0232285292
## stat191 -3.967167e-02 -3.145307e-02 -0.0139988508 0.0742796869 0.0362291443 -0.1054385942
## stat192 -5.345331e-02 6.153848e-02 0.0523396421 0.0431895438 -0.1306709619 -0.0309666575
## stat193 -6.772250e-02 -3.547342e-02 -0.0363198745 0.0474709135 -0.0710457364 0.0020269016
## stat194 -1.889942e-02 -9.312420e-02 0.0566993199 0.0175508938 -0.1211513725 0.0689506624
## stat195 6.431426e-02 1.361193e-02 0.0089859324 0.0806589909 0.0075709681 0.0385048505
## stat196 3.433283e-02 -1.237059e-01 -0.0834179752 0.0430138558 0.0023430247 -0.0009756640
## stat197 6.664547e-02 7.512493e-02 -0.0461451185 0.1656166329 0.0479003268 -0.0634346704
## stat198 9.912890e-02 5.898018e-02 -0.0194289915 -0.0450723682 -0.1072002427 0.0405216788
## stat199 -4.536366e-02 4.235294e-02 -0.0434677843 -0.1070801116 -0.0538184989 -0.0353472107
## stat200 1.275497e-01 -3.153857e-02 -0.1619824250 -0.0676535536 0.0585896417 -0.1621891088
## stat201 7.571836e-02 -2.132856e-02 0.1244190262 0.0560608625 0.0876772723 0.0431733428
## stat202 8.327428e-02 9.900851e-02 0.0143901531 -0.0367695730 -0.0324374914 0.0516051469
## stat203 3.425612e-02 8.535592e-02 0.0520798278 -0.0653485149 0.0451075032 -0.0239492102
## stat204 1.708797e-01 1.244003e-01 -0.0960761090 -0.0833868563 -0.0216612082 0.0158732112
## stat205 7.395627e-03 -7.583697e-02 0.0339318937 0.0408766578 -0.0441586723 0.1478506778
## stat206 1.132621e-01 -6.287358e-02 0.0164864330 0.0849883886 -0.0929190254 0.0075770289
## stat207 6.454215e-02 1.560668e-03 0.1492843782 0.0325684988 0.0103621776 -0.0050873524
## stat208 -3.231587e-02 -4.794680e-02 0.0206205174 0.0308789917 -0.0965091889 0.0129358338
## stat209 2.761043e-02 -3.176905e-02 -0.1441484116 0.1465193632 0.0710740277 -0.0090005731
## stat210 4.449593e-02 -3.371789e-02 -0.1270521367 0.0840603190 0.0690742011 -0.0759119492
## stat211 -3.193365e-02 5.057500e-02 0.0039105900 -0.0940116622 -0.0624037534 -0.0279503241
## stat212 2.640972e-02 3.000265e-03 -0.0616115700 -0.0705095823 0.0377682339 -0.1083317823
## stat213 1.609179e-02 1.457910e-02 0.0620487519 -0.0965103037 0.0144320861 0.0929282180
## stat214 -1.181161e-01 -1.874195e-02 -0.0416693943 0.0570788085 0.0598268280 0.0254916200
## stat215 -4.534195e-03 4.081127e-02 0.0664891471 0.0681805891 0.0748518199 -0.0787665624
## stat216 -4.341201e-02 -1.087404e-01 0.0190007930 -0.0132950509 0.1468583341 -0.0418279750
## stat217 1.395179e-02 -1.420540e-02 -0.0871605432 0.0805098615 -0.0755356434 0.0068908325
## x18.sqrt 4.149242e-02 -9.784938e-02 0.0638694348 0.0066699312 0.0025306088 -0.0641368027#creating dataset
data.pca = dplyr::select(data,!!label.names) %>%
dplyr::bind_cols(dplyr::select(as.data.frame(pca.model$x)
,!!colnames(pca.model$rotation)[pca.model$pcaSel])
)Train Test Split
data.pca = data[sample(nrow(data.pca)),] # randomly shuffle data
split = sample.split(data.pca[,label.names], SplitRatio = 0.8)
data.train = subset(data.pca, split == TRUE)
data.test = subset(data.pca, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
df = data.frame(x=predict(model,train),y=r.student)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = 0,size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
df = data.frame(x=predict(model,train),y=r.standard)
p=ggplot(data=df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_hline(yintercept = c(-2,0,2),size=1)+
ylab("Student Residuals") +
xlab("Predicted Values")+
ggtitle("Student Residual Plot")
plot(p)
# Histogram
df=data.frame(r.student)
p=ggplot(data=df,aes(r.student)) +
geom_histogram(aes(y=..density..),bins = 50,fill='blue',alpha=0.6) +
stat_function(fun = dnorm, n = 100, args = list(mean = 0, sd = 1)) +
ylab("Density")+
xlab("Studentized Residuals")+
ggtitle("Distribution of Studentized Residuals")
plot(p)
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
df=tibble::rownames_to_column(as.data.frame(lev),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=lev)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
ylab('Leverage - check') +
xlab('Index')
plot(p)
# Cook's Distance
cd = cooks.distance(model)
df=tibble::rownames_to_column(as.data.frame(cd),'id')
p=ggplot(data=df,aes(x=as.numeric(id),y=cd)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_text(data=filter(df,cd>15/nrow(train)),aes(label=id),check_overlap=T,size=3,vjust=-.5)+
ylab('Cooks distances') +
geom_hline(yintercept = c(4/nrow(train),0),size=1)+
xlab('Index')
plot(p)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
# function to set up random seeds
# Based on http://jaehyeon-kim.github.io/2015/05/Setup-Random-Seeds-on-Caret-Package.html
setCaretSeeds <- function(method = "cv", numbers = 1, repeats = 1, tunes = NULL, seed = 1701) {
#B is the number of resamples and integer vector of M (numbers + tune length if any)
B <- if (method == "cv") numbers
else if(method == "repeatedcv") numbers * repeats
else NULL
if(is.null(length)) {
seeds <- NULL
} else {
set.seed(seed = seed)
seeds <- vector(mode = "list", length = B)
seeds <- lapply(seeds, function(x) sample.int(n = 1000000
, size = numbers + ifelse(is.null(tunes), 0, tunes)))
seeds[[length(seeds) + 1]] <- sample.int(n = 1000000, size = 1)
}
# return seeds
seeds
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,seeds = setCaretSeeds(method = "cv"
, numbers = 10
, seed = 1701)
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
cl <- makeCluster(ceiling(detectCores()*0.85)) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print("All models results")
print(model.caret$results) # all model results
print("Best Model")
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-nvmax) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=nvmax,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
# leap function does not support studentized residuals
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
id = rownames(model.caret$bestTune)
# Provides the coefficients of the best model
# regsubsets doens return a full model (see documentation of regsubset), so we need to recalcualte themodel
# https://stackoverflow.com/questions/13063762/how-to-obtain-a-lm-object-from-regsubsets
print("Coefficients of final model:")
coefs <- coef(model, id=id)
#calculate the model to the the coef intervals
nams <- names(coefs)
nams <- nams[!nams %in% "(Intercept)"]
response <- as.character(formula[[2]])
form <- as.formula(paste(response, paste(nams, collapse = " + "), sep = " ~ "))
mod <- lm(form, data = data)
#coefs
#coef(mod)
print(car::Confint(mod))
return(list(model = model,id = id, residPlot = residPlot, residHistogram=residHistogram
,modelLM=mod))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
print(model.caret$results)
model=model.caret$finalModel
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-lambda) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=lambda,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
#no interval for glmnet: https://stackoverflow.com/questions/39750965/confidence-intervals-for-ridge-regression
t=coef(model,s=model.caret$bestTune$lambda)
model.coef = t[which(t[,1]!=0),]
print(as.data.frame(model.coef))
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, metricsPlot=metricsPlot ))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Metrics Plot
dataPlot = model.caret$results %>%
gather(key='metric',value='value',-fraction) %>%
dplyr::filter(metric %in% c('MAE','RMSE','Rsquared'))
metricsPlot = ggplot(data=dataPlot,aes(x=fraction,y=value) ) +
geom_line(color='lightblue4') +
geom_point(color='blue',alpha=0.7,size=.9) +
facet_wrap(~metric,ncol=2,scales='free_y')+
theme_light()
plot(metricsPlot)
# Residuals Plot
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth(method="lm")+
theme_light()
plot(residPlot)
residHistogram = ggplot(dataPlot,aes(x=res)) +
geom_histogram(aes(y=..density..),fill='light blue',alpha=1) +
#geom_density(color='lightblue4') +
stat_function(fun = dnorm, n = 100, args = list(mean = mean(dataPlot$res)
, sd = sd(dataPlot$res)),color='lightblue4')
theme_light()
plot(residHistogram)
print("Coefficients")
t=coef(model.caret$finalModel,s=model.caret$bestTune$fraction,mode='fraction')
model.coef = t[which(t!=0)]
print(model.coef)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id, residPlot = residPlot, residHistogram=residHistogram))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changed slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names
,transformation = NULL){
## if using caret for glm select equivalent functionality,
## need to pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
if(log.pred == TRUE || norm.pred == TRUE){
# plot transformewd comparison first
df=data.frame(x=test[,label.names],y=pred[,1])
ggplot(df,aes(x=x,y=y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=1,intercept=0,color='black',size=1) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual (Transformed)")+
ylab("Predicted (Transformed)")
}
if (log.pred == FALSE && norm.pred == FALSE){
x = test[,label.names]
y = pred[,1]
}
if (log.pred == TRUE){
x = 10^test[,label.names]
y = 10^pred[,1]
}
if (norm.pred == TRUE){
x = predict(transformation, test[,label.names], inverse = TRUE)
y = predict(transformation, pred[,1], inverse = TRUE)
}
df=data.frame(x,y)
ggplot(df,aes(x,y)) +
geom_point(color='blue',alpha=0.5,shape=20,size=2) +
geom_abline(slope=c(1+good,1-good,1+ok,1-ok)
,intercept=rep(0,4),color=c('dark green','dark green','dark red','dark red'),size=1,alpha=0.8) +
#scale_y_continuous(limits=c(min(df),max(df)))+
xlab("Actual")+
ylab("Predicted")
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")
," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3.log ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 +
## x12 + x13 + x14 + x15 + x16 + x17 + x19 + x20 + x21 + x22 +
## x23 + stat1 + stat2 + stat3 + stat4 + stat5 + stat6 + stat7 +
## stat8 + stat9 + stat10 + stat11 + stat12 + stat13 + stat14 +
## stat15 + stat16 + stat17 + stat18 + stat19 + stat20 + stat21 +
## stat22 + stat23 + stat24 + stat25 + stat26 + stat27 + stat28 +
## stat29 + stat30 + stat31 + stat32 + stat33 + stat34 + stat35 +
## stat36 + stat37 + stat38 + stat39 + stat40 + stat41 + stat42 +
## stat43 + stat44 + stat45 + stat46 + stat47 + stat48 + stat49 +
## stat50 + stat51 + stat52 + stat53 + stat54 + stat55 + stat56 +
## stat57 + stat58 + stat59 + stat60 + stat61 + stat62 + stat63 +
## stat64 + stat65 + stat66 + stat67 + stat68 + stat69 + stat70 +
## stat71 + stat72 + stat73 + stat74 + stat75 + stat76 + stat77 +
## stat78 + stat79 + stat80 + stat81 + stat82 + stat83 + stat84 +
## stat85 + stat86 + stat87 + stat88 + stat89 + stat90 + stat91 +
## stat92 + stat93 + stat94 + stat95 + stat96 + stat97 + stat98 +
## stat99 + stat100 + stat101 + stat102 + stat103 + stat104 +
## stat105 + stat106 + stat107 + stat108 + stat109 + stat110 +
## stat111 + stat112 + stat113 + stat114 + stat115 + stat116 +
## stat117 + stat118 + stat119 + stat120 + stat121 + stat122 +
## stat123 + stat124 + stat125 + stat126 + stat127 + stat128 +
## stat129 + stat130 + stat131 + stat132 + stat133 + stat134 +
## stat135 + stat136 + stat137 + stat138 + stat139 + stat140 +
## stat141 + stat142 + stat143 + stat144 + stat145 + stat146 +
## stat147 + stat148 + stat149 + stat150 + stat151 + stat152 +
## stat153 + stat154 + stat155 + stat156 + stat157 + stat158 +
## stat159 + stat160 + stat161 + stat162 + stat163 + stat164 +
## stat165 + stat166 + stat167 + stat168 + stat169 + stat170 +
## stat171 + stat172 + stat173 + stat174 + stat175 + stat176 +
## stat177 + stat178 + stat179 + stat180 + stat181 + stat182 +
## stat183 + stat184 + stat185 + stat186 + stat187 + stat188 +
## stat189 + stat190 + stat191 + stat192 + stat193 + stat194 +
## stat195 + stat196 + stat197 + stat198 + stat199 + stat200 +
## stat201 + stat202 + stat203 + stat204 + stat205 + stat206 +
## stat207 + stat208 + stat209 + stat210 + stat211 + stat212 +
## stat213 + stat214 + stat215 + stat216 + stat217 + x18.sqrtprint(grand.mean.formula)## y3.log ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.087790 -0.020521 -0.004714 0.016662 0.159351
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.970e+00 9.469e-03 208.031 < 2e-16 ***
## x1 -6.875e-05 6.514e-04 -0.106 0.915943
## x2 4.046e-04 4.177e-04 0.969 0.332785
## x3 2.609e-05 1.142e-04 0.228 0.819343
## x4 -5.445e-05 9.015e-06 -6.040 1.65e-09 ***
## x5 3.372e-04 2.952e-04 1.142 0.253437
## x6 5.357e-04 5.952e-04 0.900 0.368142
## x7 1.138e-02 6.377e-04 17.842 < 2e-16 ***
## x8 3.744e-04 1.480e-04 2.530 0.011439 *
## x9 3.188e-03 3.305e-04 9.646 < 2e-16 ***
## x10 1.111e-03 3.079e-04 3.609 0.000310 ***
## x11 1.714e+05 7.327e+04 2.340 0.019332 *
## x12 -1.744e-04 1.883e-04 -0.926 0.354398
## x13 5.803e-05 7.474e-05 0.776 0.437570
## x14 -4.724e-04 3.222e-04 -1.466 0.142617
## x15 3.963e-04 3.081e-04 1.286 0.198366
## x16 7.984e-04 2.126e-04 3.755 0.000175 ***
## x17 1.432e-03 3.243e-04 4.416 1.02e-05 ***
## x19 1.729e-04 1.652e-04 1.047 0.295369
## x20 -6.344e-04 1.148e-03 -0.553 0.580448
## x21 1.445e-04 4.198e-05 3.442 0.000581 ***
## x22 -3.157e-04 3.443e-04 -0.917 0.359213
## x23 4.404e-05 3.286e-04 0.134 0.893385
## stat1 -1.822e-04 2.483e-04 -0.734 0.462967
## stat2 1.467e-04 2.461e-04 0.596 0.551067
## stat3 3.431e-04 2.473e-04 1.387 0.165437
## stat4 -5.715e-04 2.486e-04 -2.299 0.021552 *
## stat5 -3.114e-04 2.474e-04 -1.259 0.208167
## stat6 -2.738e-04 2.476e-04 -1.106 0.268768
## stat7 -1.120e-04 2.482e-04 -0.451 0.651817
## stat8 2.294e-04 2.489e-04 0.922 0.356831
## stat9 6.876e-05 2.461e-04 0.279 0.779934
## stat10 -3.776e-05 2.473e-04 -0.153 0.878631
## stat11 -2.589e-04 2.509e-04 -1.032 0.302085
## stat12 1.796e-04 2.481e-04 0.724 0.469286
## stat13 -5.746e-04 2.453e-04 -2.343 0.019169 *
## stat14 -1.001e-03 2.469e-04 -4.053 5.12e-05 ***
## stat15 -1.434e-04 2.453e-04 -0.584 0.558915
## stat16 -2.676e-05 2.481e-04 -0.108 0.914127
## stat17 -2.092e-04 2.454e-04 -0.852 0.394052
## stat18 -1.851e-04 2.469e-04 -0.750 0.453549
## stat19 7.791e-05 2.446e-04 0.319 0.750095
## stat20 -3.289e-04 2.473e-04 -1.330 0.183586
## stat21 -1.824e-04 2.476e-04 -0.737 0.461407
## stat22 -4.280e-04 2.467e-04 -1.735 0.082797 .
## stat23 6.412e-04 2.462e-04 2.605 0.009223 **
## stat24 -5.935e-04 2.472e-04 -2.401 0.016375 *
## stat25 -5.027e-04 2.457e-04 -2.046 0.040790 *
## stat26 -4.465e-04 2.477e-04 -1.803 0.071510 .
## stat27 1.587e-04 2.467e-04 0.643 0.519942
## stat28 1.040e-04 2.481e-04 0.419 0.675164
## stat29 2.090e-04 2.492e-04 0.839 0.401640
## stat30 3.128e-04 2.501e-04 1.251 0.211104
## stat31 -1.615e-04 2.497e-04 -0.647 0.517700
## stat32 1.137e-05 2.506e-04 0.045 0.963807
## stat33 -2.695e-04 2.473e-04 -1.090 0.275856
## stat34 1.406e-04 2.459e-04 0.572 0.567560
## stat35 -4.585e-04 2.480e-04 -1.849 0.064565 .
## stat36 -2.043e-04 2.464e-04 -0.829 0.407034
## stat37 -5.047e-04 2.491e-04 -2.026 0.042776 *
## stat38 5.782e-05 2.485e-04 0.233 0.816027
## stat39 -1.208e-04 2.457e-04 -0.492 0.622873
## stat40 1.602e-04 2.483e-04 0.645 0.518939
## stat41 -6.164e-04 2.462e-04 -2.503 0.012331 *
## stat42 -1.103e-04 2.468e-04 -0.447 0.654990
## stat43 -3.934e-04 2.483e-04 -1.585 0.113116
## stat44 1.676e-05 2.480e-04 0.068 0.946099
## stat45 -1.565e-04 2.462e-04 -0.636 0.525053
## stat46 3.396e-04 2.473e-04 1.374 0.169646
## stat47 2.950e-04 2.494e-04 1.183 0.236878
## stat48 2.600e-04 2.467e-04 1.054 0.291971
## stat49 7.408e-05 2.460e-04 0.301 0.763343
## stat50 2.825e-04 2.448e-04 1.154 0.248659
## stat51 3.813e-04 2.475e-04 1.540 0.123536
## stat52 1.571e-04 2.479e-04 0.634 0.526284
## stat53 -2.557e-04 2.500e-04 -1.023 0.306465
## stat54 -4.243e-04 2.489e-04 -1.705 0.088316 .
## stat55 2.774e-04 2.454e-04 1.130 0.258433
## stat56 -2.860e-04 2.481e-04 -1.153 0.249030
## stat57 6.872e-05 2.446e-04 0.281 0.778717
## stat58 2.393e-04 2.446e-04 0.978 0.327948
## stat59 4.209e-04 2.487e-04 1.692 0.090687 .
## stat60 4.380e-04 2.495e-04 1.756 0.079175 .
## stat61 1.849e-06 2.480e-04 0.007 0.994051
## stat62 5.518e-05 2.472e-04 0.223 0.823371
## stat63 1.627e-04 2.504e-04 0.650 0.515850
## stat64 -1.790e-04 2.470e-04 -0.725 0.468720
## stat65 -3.782e-04 2.492e-04 -1.517 0.129200
## stat66 1.695e-04 2.527e-04 0.671 0.502278
## stat67 1.701e-04 2.477e-04 0.687 0.492327
## stat68 -6.913e-05 2.480e-04 -0.279 0.780464
## stat69 1.919e-04 2.469e-04 0.777 0.437014
## stat70 8.695e-05 2.470e-04 0.352 0.724834
## stat71 -3.863e-05 2.457e-04 -0.157 0.875043
## stat72 3.121e-04 2.479e-04 1.259 0.208067
## stat73 3.755e-04 2.495e-04 1.505 0.132334
## stat74 -2.071e-04 2.479e-04 -0.835 0.403674
## stat75 -1.151e-04 2.498e-04 -0.461 0.645096
## stat76 1.450e-04 2.468e-04 0.588 0.556866
## stat77 -2.794e-04 2.485e-04 -1.124 0.260954
## stat78 -2.863e-04 2.484e-04 -1.153 0.249060
## stat79 -6.347e-05 2.468e-04 -0.257 0.797029
## stat80 1.381e-04 2.485e-04 0.556 0.578361
## stat81 2.620e-04 2.486e-04 1.054 0.291893
## stat82 2.354e-04 2.455e-04 0.959 0.337687
## stat83 3.367e-05 2.477e-04 0.136 0.891889
## stat84 -2.227e-04 2.471e-04 -0.901 0.367382
## stat85 -1.910e-05 2.487e-04 -0.077 0.938798
## stat86 1.999e-04 2.477e-04 0.807 0.419643
## stat87 -1.903e-04 2.488e-04 -0.765 0.444466
## stat88 -1.622e-04 2.435e-04 -0.666 0.505264
## stat89 -1.810e-04 2.458e-04 -0.736 0.461559
## stat90 -3.024e-04 2.484e-04 -1.217 0.223580
## stat91 -5.075e-04 2.454e-04 -2.068 0.038693 *
## stat92 -2.590e-04 2.473e-04 -1.047 0.295134
## stat93 -3.048e-04 2.503e-04 -1.218 0.223323
## stat94 -1.919e-04 2.479e-04 -0.774 0.438924
## stat95 3.935e-05 2.484e-04 0.158 0.874122
## stat96 -2.172e-04 2.458e-04 -0.884 0.376921
## stat97 6.804e-05 2.469e-04 0.276 0.782895
## stat98 3.507e-03 2.444e-04 14.351 < 2e-16 ***
## stat99 3.155e-04 2.488e-04 1.268 0.204754
## stat100 7.802e-04 2.465e-04 3.165 0.001560 **
## stat101 -2.134e-04 2.503e-04 -0.853 0.393756
## stat102 1.265e-04 2.489e-04 0.508 0.611404
## stat103 -3.971e-04 2.490e-04 -1.594 0.110892
## stat104 -4.051e-04 2.464e-04 -1.644 0.100139
## stat105 4.281e-04 2.460e-04 1.740 0.081925 .
## stat106 -3.522e-04 2.462e-04 -1.431 0.152601
## stat107 -1.174e-05 2.459e-04 -0.048 0.961921
## stat108 -2.974e-04 2.466e-04 -1.206 0.227981
## stat109 -4.193e-06 2.457e-04 -0.017 0.986385
## stat110 -3.298e-03 2.459e-04 -13.411 < 2e-16 ***
## stat111 -1.204e-04 2.470e-04 -0.488 0.625836
## stat112 -2.939e-04 2.502e-04 -1.175 0.240151
## stat113 -2.056e-04 2.484e-04 -0.828 0.407880
## stat114 3.119e-04 2.464e-04 1.266 0.205729
## stat115 7.628e-05 2.476e-04 0.308 0.757998
## stat116 1.780e-04 2.489e-04 0.715 0.474476
## stat117 6.357e-05 2.484e-04 0.256 0.798054
## stat118 -2.053e-04 2.460e-04 -0.834 0.404175
## stat119 4.778e-05 2.469e-04 0.194 0.846534
## stat120 8.390e-05 2.462e-04 0.341 0.733310
## stat121 -2.703e-04 2.475e-04 -1.092 0.274827
## stat122 -3.042e-04 2.463e-04 -1.235 0.216861
## stat123 5.896e-06 2.500e-04 0.024 0.981183
## stat124 -1.755e-04 2.473e-04 -0.710 0.477952
## stat125 -1.152e-05 2.481e-04 -0.046 0.962962
## stat126 1.528e-04 2.452e-04 0.623 0.533335
## stat127 4.626e-05 2.479e-04 0.187 0.851982
## stat128 6.080e-05 2.476e-04 0.246 0.806030
## stat129 2.103e-04 2.466e-04 0.853 0.393691
## stat130 2.428e-04 2.485e-04 0.977 0.328519
## stat131 3.363e-04 2.483e-04 1.354 0.175643
## stat132 -9.678e-05 2.470e-04 -0.392 0.695204
## stat133 -1.024e-04 2.471e-04 -0.414 0.678605
## stat134 -1.514e-04 2.467e-04 -0.614 0.539384
## stat135 2.167e-05 2.473e-04 0.088 0.930164
## stat136 5.831e-05 2.475e-04 0.236 0.813721
## stat137 1.727e-05 2.459e-04 0.070 0.944004
## stat138 6.790e-05 2.476e-04 0.274 0.783895
## stat139 2.208e-04 2.494e-04 0.885 0.376007
## stat140 6.425e-06 2.462e-04 0.026 0.979184
## stat141 1.313e-04 2.473e-04 0.531 0.595450
## stat142 1.174e-04 2.502e-04 0.469 0.639021
## stat143 4.126e-05 2.476e-04 0.167 0.867656
## stat144 3.594e-04 2.465e-04 1.458 0.144853
## stat145 -7.790e-05 2.512e-04 -0.310 0.756455
## stat146 -4.421e-04 2.483e-04 -1.781 0.075043 .
## stat147 -2.573e-04 2.512e-04 -1.024 0.305699
## stat148 -3.464e-04 2.442e-04 -1.418 0.156188
## stat149 -6.713e-04 2.488e-04 -2.698 0.006996 **
## stat150 5.836e-05 2.481e-04 0.235 0.814036
## stat151 -2.212e-04 2.492e-04 -0.888 0.374742
## stat152 -1.464e-04 2.469e-04 -0.593 0.553307
## stat153 -2.034e-04 2.518e-04 -0.808 0.419180
## stat154 7.513e-05 2.485e-04 0.302 0.762392
## stat155 -3.400e-04 2.467e-04 -1.379 0.168094
## stat156 5.754e-04 2.509e-04 2.294 0.021840 *
## stat157 -9.609e-05 2.453e-04 -0.392 0.695235
## stat158 6.422e-05 2.506e-04 0.256 0.797769
## stat159 5.681e-05 2.453e-04 0.232 0.816876
## stat160 1.849e-04 2.489e-04 0.743 0.457755
## stat161 1.828e-04 2.482e-04 0.736 0.461575
## stat162 -1.556e-04 2.450e-04 -0.635 0.525334
## stat163 -4.061e-05 2.498e-04 -0.163 0.870895
## stat164 1.986e-04 2.497e-04 0.795 0.426392
## stat165 -2.873e-04 2.447e-04 -1.174 0.240451
## stat166 -3.691e-05 2.457e-04 -0.150 0.880583
## stat167 -7.926e-05 2.468e-04 -0.321 0.748084
## stat168 -2.477e-04 2.460e-04 -1.007 0.314129
## stat169 -1.262e-04 2.479e-04 -0.509 0.610834
## stat170 -2.508e-04 2.475e-04 -1.013 0.311026
## stat171 2.669e-04 2.498e-04 1.069 0.285241
## stat172 1.535e-04 2.470e-04 0.622 0.534134
## stat173 -2.550e-04 2.490e-04 -1.024 0.305824
## stat174 2.071e-04 2.486e-04 0.833 0.405035
## stat175 -3.037e-04 2.480e-04 -1.225 0.220714
## stat176 1.699e-04 2.476e-04 0.686 0.492557
## stat177 -6.734e-05 2.478e-04 -0.272 0.785837
## stat178 -1.873e-04 2.497e-04 -0.750 0.453234
## stat179 -2.269e-05 2.465e-04 -0.092 0.926662
## stat180 -3.943e-04 2.454e-04 -1.607 0.108183
## stat181 2.956e-04 2.499e-04 1.183 0.237021
## stat182 1.180e-04 2.491e-04 0.474 0.635838
## stat183 2.252e-04 2.450e-04 0.919 0.357992
## stat184 -3.300e-05 2.490e-04 -0.133 0.894557
## stat185 -4.606e-06 2.456e-04 -0.019 0.985039
## stat186 -2.337e-04 2.491e-04 -0.938 0.348180
## stat187 -2.899e-04 2.461e-04 -1.178 0.238771
## stat188 -1.494e-04 2.466e-04 -0.606 0.544589
## stat189 1.148e-04 2.479e-04 0.463 0.643194
## stat190 1.268e-04 2.470e-04 0.513 0.607734
## stat191 -4.050e-04 2.486e-04 -1.629 0.103337
## stat192 -1.126e-04 2.484e-04 -0.453 0.650520
## stat193 4.553e-07 2.502e-04 0.002 0.998548
## stat194 8.995e-05 2.463e-04 0.365 0.715034
## stat195 3.262e-04 2.473e-04 1.319 0.187149
## stat196 -1.622e-04 2.501e-04 -0.648 0.516725
## stat197 1.417e-04 2.451e-04 0.578 0.563201
## stat198 -2.471e-04 2.476e-04 -0.998 0.318254
## stat199 -2.617e-05 2.461e-04 -0.106 0.915317
## stat200 -8.303e-05 2.446e-04 -0.339 0.734313
## stat201 -2.069e-04 2.466e-04 -0.839 0.401434
## stat202 -3.130e-04 2.495e-04 -1.255 0.209705
## stat203 1.458e-04 2.483e-04 0.587 0.557160
## stat204 -6.651e-04 2.459e-04 -2.704 0.006866 **
## stat205 -9.348e-05 2.471e-04 -0.378 0.705250
## stat206 3.486e-05 2.492e-04 0.140 0.888753
## stat207 2.672e-04 2.463e-04 1.085 0.278069
## stat208 1.457e-04 2.479e-04 0.588 0.556706
## stat209 -2.876e-04 2.459e-04 -1.169 0.242309
## stat210 6.745e-05 2.486e-04 0.271 0.786126
## stat211 1.573e-05 2.466e-04 0.064 0.949143
## stat212 -1.182e-04 2.470e-04 -0.479 0.632303
## stat213 -3.536e-04 2.496e-04 -1.416 0.156712
## stat214 -3.929e-04 2.487e-04 -1.580 0.114210
## stat215 -1.864e-04 2.464e-04 -0.756 0.449394
## stat216 -9.204e-05 2.475e-04 -0.372 0.709991
## stat217 4.742e-04 2.484e-04 1.909 0.056280 .
## x18.sqrt 2.660e-02 9.477e-04 28.072 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03134 on 5343 degrees of freedom
## Multiple R-squared: 0.272, Adjusted R-squared: 0.2393
## F-statistic: 8.317 on 240 and 5343 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model=model.full, train=data.train)
## [1] "Number of data points that have Cook's D > 4/n: 288"
## [1] "Number of data points that have Cook's D > 1: 0"Checking with removal of high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
#save dataset with high.cd flagged
t = data.train %>%
rownames_to_column() %>%
mutate(high.cd = ifelse(rowname %in% high.cd,1,0))
write.csv(t,file='data_high_cd_flag.csv',row.names = F)
###
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.057191 -0.017273 -0.002512 0.016683 0.071119
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.958e+00 7.804e-03 250.888 < 2e-16 ***
## x1 -2.153e-04 5.368e-04 -0.401 0.68834
## x2 4.797e-04 3.432e-04 1.398 0.16229
## x3 -2.247e-05 9.355e-05 -0.240 0.81015
## x4 -5.830e-05 7.433e-06 -7.844 5.29e-15 ***
## x5 5.739e-04 2.421e-04 2.370 0.01782 *
## x6 1.762e-04 4.893e-04 0.360 0.71879
## x7 1.195e-02 5.245e-04 22.779 < 2e-16 ***
## x8 5.157e-04 1.218e-04 4.234 2.34e-05 ***
## x9 3.241e-03 2.712e-04 11.949 < 2e-16 ***
## x10 1.508e-03 2.535e-04 5.950 2.87e-09 ***
## x11 1.941e+05 6.039e+04 3.213 0.00132 **
## x12 7.673e-05 1.545e-04 0.497 0.61946
## x13 1.114e-04 6.149e-05 1.811 0.07019 .
## x14 -2.515e-04 2.645e-04 -0.951 0.34161
## x15 3.666e-04 2.524e-04 1.452 0.14645
## x16 7.824e-04 1.749e-04 4.474 7.84e-06 ***
## x17 1.475e-03 2.665e-04 5.536 3.26e-08 ***
## x19 1.449e-04 1.357e-04 1.068 0.28550
## x20 -9.261e-04 9.450e-04 -0.980 0.32714
## x21 1.363e-04 3.448e-05 3.952 7.84e-05 ***
## x22 -3.502e-04 2.825e-04 -1.240 0.21518
## x23 2.982e-04 2.706e-04 1.102 0.27056
## stat1 -1.789e-04 2.036e-04 -0.879 0.37959
## stat2 3.537e-04 2.020e-04 1.751 0.08008 .
## stat3 3.184e-04 2.035e-04 1.565 0.11762
## stat4 -6.669e-04 2.050e-04 -3.254 0.00115 **
## stat5 -3.027e-04 2.035e-04 -1.488 0.13684
## stat6 -4.424e-04 2.032e-04 -2.177 0.02953 *
## stat7 -2.132e-04 2.035e-04 -1.047 0.29495
## stat8 1.243e-05 2.045e-04 0.061 0.95151
## stat9 3.033e-05 2.022e-04 0.150 0.88081
## stat10 4.248e-06 2.025e-04 0.021 0.98326
## stat11 -2.815e-04 2.060e-04 -1.366 0.17189
## stat12 2.009e-04 2.038e-04 0.986 0.32412
## stat13 -5.151e-04 2.013e-04 -2.559 0.01054 *
## stat14 -1.103e-03 2.029e-04 -5.435 5.75e-08 ***
## stat15 -3.862e-04 2.019e-04 -1.913 0.05578 .
## stat16 -1.842e-04 2.035e-04 -0.905 0.36531
## stat17 -2.617e-04 2.021e-04 -1.295 0.19536
## stat18 -9.741e-05 2.028e-04 -0.480 0.63099
## stat19 7.765e-05 2.016e-04 0.385 0.70014
## stat20 1.682e-04 2.032e-04 0.828 0.40787
## stat21 -1.355e-04 2.035e-04 -0.666 0.50549
## stat22 -3.244e-04 2.023e-04 -1.603 0.10895
## stat23 6.712e-04 2.028e-04 3.310 0.00094 ***
## stat24 -6.094e-04 2.033e-04 -2.998 0.00273 **
## stat25 -4.335e-04 2.022e-04 -2.144 0.03207 *
## stat26 -5.229e-04 2.040e-04 -2.563 0.01039 *
## stat27 1.550e-04 2.035e-04 0.762 0.44627
## stat28 8.251e-05 2.041e-04 0.404 0.68608
## stat29 1.722e-04 2.048e-04 0.841 0.40049
## stat30 1.523e-04 2.053e-04 0.742 0.45807
## stat31 -9.278e-06 2.051e-04 -0.045 0.96391
## stat32 2.850e-05 2.064e-04 0.138 0.89016
## stat33 -1.402e-04 2.031e-04 -0.690 0.49007
## stat34 3.622e-04 2.024e-04 1.790 0.07356 .
## stat35 -5.216e-04 2.040e-04 -2.557 0.01058 *
## stat36 -1.924e-04 2.026e-04 -0.950 0.34227
## stat37 -2.170e-04 2.048e-04 -1.060 0.28924
## stat38 1.122e-04 2.037e-04 0.551 0.58172
## stat39 -9.340e-05 2.018e-04 -0.463 0.64354
## stat40 7.828e-05 2.046e-04 0.383 0.70204
## stat41 -6.465e-04 2.021e-04 -3.198 0.00139 **
## stat42 -1.031e-04 2.030e-04 -0.508 0.61153
## stat43 -3.425e-04 2.041e-04 -1.678 0.09349 .
## stat44 2.995e-05 2.039e-04 0.147 0.88322
## stat45 -1.072e-04 2.021e-04 -0.530 0.59584
## stat46 7.285e-05 2.035e-04 0.358 0.72043
## stat47 4.319e-04 2.049e-04 2.108 0.03505 *
## stat48 2.849e-04 2.023e-04 1.409 0.15898
## stat49 -1.676e-04 2.023e-04 -0.829 0.40729
## stat50 2.698e-04 2.012e-04 1.341 0.17992
## stat51 1.722e-04 2.036e-04 0.846 0.39772
## stat52 1.638e-04 2.037e-04 0.804 0.42153
## stat53 -3.143e-04 2.056e-04 -1.529 0.12639
## stat54 -3.946e-04 2.049e-04 -1.926 0.05417 .
## stat55 4.763e-05 2.019e-04 0.236 0.81351
## stat56 -1.236e-04 2.038e-04 -0.606 0.54444
## stat57 -1.106e-04 2.015e-04 -0.549 0.58298
## stat58 2.664e-04 2.005e-04 1.329 0.18383
## stat59 3.894e-04 2.046e-04 1.903 0.05710 .
## stat60 4.578e-04 2.049e-04 2.234 0.02550 *
## stat61 -8.386e-05 2.038e-04 -0.411 0.68074
## stat62 -1.192e-04 2.026e-04 -0.588 0.55644
## stat63 2.142e-04 2.057e-04 1.041 0.29778
## stat64 1.061e-04 2.026e-04 0.524 0.60048
## stat65 -1.878e-04 2.048e-04 -0.917 0.35927
## stat66 1.631e-04 2.076e-04 0.786 0.43207
## stat67 2.707e-04 2.036e-04 1.330 0.18360
## stat68 -1.494e-04 2.038e-04 -0.733 0.46358
## stat69 -5.792e-05 2.032e-04 -0.285 0.77559
## stat70 1.270e-04 2.029e-04 0.626 0.53139
## stat71 1.222e-04 2.024e-04 0.603 0.54625
## stat72 2.010e-04 2.036e-04 0.987 0.32356
## stat73 3.781e-04 2.057e-04 1.838 0.06616 .
## stat74 -7.996e-05 2.039e-04 -0.392 0.69492
## stat75 1.245e-04 2.052e-04 0.607 0.54401
## stat76 1.137e-04 2.028e-04 0.561 0.57514
## stat77 4.593e-07 2.043e-04 0.002 0.99821
## stat78 -5.097e-04 2.035e-04 -2.504 0.01230 *
## stat79 1.187e-04 2.023e-04 0.587 0.55742
## stat80 1.883e-04 2.040e-04 0.923 0.35609
## stat81 1.901e-04 2.045e-04 0.930 0.35246
## stat82 7.349e-05 2.020e-04 0.364 0.71596
## stat83 5.446e-05 2.033e-04 0.268 0.78881
## stat84 -2.118e-04 2.031e-04 -1.043 0.29711
## stat85 -4.218e-04 2.047e-04 -2.060 0.03942 *
## stat86 2.840e-04 2.039e-04 1.393 0.16378
## stat87 -1.339e-04 2.040e-04 -0.656 0.51160
## stat88 1.129e-06 2.004e-04 0.006 0.99551
## stat89 7.160e-05 2.024e-04 0.354 0.72352
## stat90 -3.964e-04 2.040e-04 -1.943 0.05209 .
## stat91 -4.711e-04 2.010e-04 -2.344 0.01912 *
## stat92 -1.594e-04 2.029e-04 -0.786 0.43219
## stat93 -1.931e-04 2.064e-04 -0.935 0.34964
## stat94 -1.522e-04 2.028e-04 -0.750 0.45303
## stat95 2.656e-04 2.045e-04 1.299 0.19402
## stat96 -1.959e-04 2.022e-04 -0.969 0.33281
## stat97 2.543e-04 2.028e-04 1.254 0.20980
## stat98 3.405e-03 2.010e-04 16.935 < 2e-16 ***
## stat99 4.557e-04 2.046e-04 2.228 0.02594 *
## stat100 8.089e-04 2.027e-04 3.991 6.66e-05 ***
## stat101 -2.299e-05 2.058e-04 -0.112 0.91106
## stat102 1.210e-04 2.049e-04 0.591 0.55478
## stat103 -4.278e-04 2.042e-04 -2.095 0.03620 *
## stat104 -3.061e-04 2.031e-04 -1.507 0.13184
## stat105 4.465e-04 2.024e-04 2.206 0.02746 *
## stat106 -3.900e-04 2.021e-04 -1.930 0.05367 .
## stat107 -4.123e-05 2.020e-04 -0.204 0.83830
## stat108 -3.134e-04 2.029e-04 -1.544 0.12255
## stat109 -1.372e-04 2.020e-04 -0.679 0.49711
## stat110 -3.208e-03 2.019e-04 -15.886 < 2e-16 ***
## stat111 -1.495e-04 2.025e-04 -0.738 0.46042
## stat112 -4.427e-04 2.060e-04 -2.149 0.03171 *
## stat113 -1.650e-05 2.040e-04 -0.081 0.93556
## stat114 3.056e-04 2.027e-04 1.508 0.13168
## stat115 2.109e-07 2.036e-04 0.001 0.99917
## stat116 1.316e-04 2.046e-04 0.643 0.51997
## stat117 -9.500e-05 2.038e-04 -0.466 0.64122
## stat118 1.246e-04 2.021e-04 0.617 0.53751
## stat119 2.238e-04 2.026e-04 1.104 0.26955
## stat120 9.639e-07 2.025e-04 0.005 0.99620
## stat121 -2.081e-04 2.035e-04 -1.023 0.30651
## stat122 -1.978e-04 2.028e-04 -0.975 0.32942
## stat123 2.194e-04 2.053e-04 1.069 0.28516
## stat124 -2.777e-04 2.031e-04 -1.367 0.17155
## stat125 -6.277e-05 2.039e-04 -0.308 0.75819
## stat126 2.175e-04 2.015e-04 1.079 0.28049
## stat127 -9.208e-05 2.033e-04 -0.453 0.65071
## stat128 -2.145e-04 2.034e-04 -1.055 0.29166
## stat129 2.281e-04 2.025e-04 1.127 0.25990
## stat130 1.169e-04 2.040e-04 0.573 0.56659
## stat131 2.712e-04 2.035e-04 1.332 0.18277
## stat132 -1.317e-04 2.029e-04 -0.649 0.51648
## stat133 1.149e-04 2.035e-04 0.564 0.57255
## stat134 -3.503e-05 2.025e-04 -0.173 0.86262
## stat135 -1.150e-04 2.031e-04 -0.566 0.57152
## stat136 -2.122e-05 2.031e-04 -0.104 0.91679
## stat137 1.985e-04 2.020e-04 0.983 0.32567
## stat138 -1.656e-05 2.035e-04 -0.081 0.93513
## stat139 3.385e-05 2.051e-04 0.165 0.86890
## stat140 5.464e-05 2.022e-04 0.270 0.78694
## stat141 2.350e-04 2.030e-04 1.158 0.24700
## stat142 1.757e-04 2.059e-04 0.853 0.39364
## stat143 1.477e-05 2.039e-04 0.072 0.94224
## stat144 4.040e-04 2.026e-04 1.994 0.04619 *
## stat145 -2.367e-05 2.067e-04 -0.115 0.90883
## stat146 -5.328e-04 2.039e-04 -2.614 0.00899 **
## stat147 -1.616e-04 2.067e-04 -0.782 0.43435
## stat148 -2.228e-04 2.008e-04 -1.109 0.26735
## stat149 -7.558e-04 2.050e-04 -3.687 0.00023 ***
## stat150 -2.100e-04 2.042e-04 -1.028 0.30382
## stat151 1.472e-04 2.051e-04 0.718 0.47297
## stat152 -2.149e-04 2.027e-04 -1.060 0.28912
## stat153 1.519e-04 2.065e-04 0.736 0.46194
## stat154 2.831e-04 2.046e-04 1.383 0.16668
## stat155 -2.079e-04 2.029e-04 -1.025 0.30558
## stat156 4.035e-04 2.059e-04 1.959 0.05012 .
## stat157 -1.269e-04 2.015e-04 -0.630 0.52870
## stat158 2.408e-04 2.058e-04 1.170 0.24199
## stat159 1.591e-04 2.016e-04 0.789 0.43002
## stat160 5.330e-05 2.050e-04 0.260 0.79490
## stat161 1.407e-04 2.043e-04 0.689 0.49100
## stat162 -6.442e-06 2.009e-04 -0.032 0.97442
## stat163 -2.909e-05 2.061e-04 -0.141 0.88780
## stat164 1.302e-04 2.055e-04 0.634 0.52635
## stat165 -9.396e-05 2.012e-04 -0.467 0.64047
## stat166 4.036e-05 2.015e-04 0.200 0.84123
## stat167 -8.971e-05 2.029e-04 -0.442 0.65842
## stat168 -2.183e-04 2.021e-04 -1.080 0.28006
## stat169 -9.377e-05 2.045e-04 -0.458 0.64662
## stat170 -5.387e-05 2.037e-04 -0.264 0.79142
## stat171 1.064e-04 2.054e-04 0.518 0.60444
## stat172 4.405e-04 2.027e-04 2.173 0.02979 *
## stat173 -2.053e-05 2.043e-04 -0.100 0.91996
## stat174 3.249e-04 2.043e-04 1.591 0.11178
## stat175 -1.044e-04 2.037e-04 -0.513 0.60822
## stat176 -1.881e-04 2.036e-04 -0.924 0.35564
## stat177 -4.450e-04 2.036e-04 -2.186 0.02883 *
## stat178 -1.377e-04 2.049e-04 -0.672 0.50173
## stat179 4.000e-05 2.025e-04 0.198 0.84339
## stat180 -2.037e-04 2.025e-04 -1.006 0.31447
## stat181 2.715e-04 2.053e-04 1.322 0.18613
## stat182 2.826e-04 2.052e-04 1.377 0.16855
## stat183 2.355e-04 2.015e-04 1.169 0.24250
## stat184 7.741e-05 2.044e-04 0.379 0.70496
## stat185 1.245e-04 2.021e-04 0.616 0.53777
## stat186 1.901e-05 2.047e-04 0.093 0.92603
## stat187 -1.916e-04 2.021e-04 -0.948 0.34314
## stat188 -1.153e-04 2.027e-04 -0.569 0.56951
## stat189 -9.714e-05 2.044e-04 -0.475 0.63456
## stat190 -5.304e-05 2.030e-04 -0.261 0.79390
## stat191 -2.952e-04 2.041e-04 -1.446 0.14819
## stat192 -1.477e-05 2.045e-04 -0.072 0.94240
## stat193 1.515e-04 2.059e-04 0.736 0.46171
## stat194 -1.569e-04 2.029e-04 -0.773 0.43932
## stat195 7.721e-05 2.036e-04 0.379 0.70457
## stat196 -1.569e-04 2.051e-04 -0.765 0.44417
## stat197 -5.094e-05 2.016e-04 -0.253 0.80052
## stat198 -2.133e-04 2.034e-04 -1.048 0.29450
## stat199 7.116e-05 2.018e-04 0.353 0.72434
## stat200 -2.118e-04 2.017e-04 -1.050 0.29370
## stat201 -1.078e-04 2.031e-04 -0.531 0.59574
## stat202 -2.108e-04 2.053e-04 -1.027 0.30447
## stat203 1.357e-04 2.041e-04 0.665 0.50626
## stat204 -2.541e-04 2.026e-04 -1.255 0.20967
## stat205 1.489e-04 2.025e-04 0.735 0.46210
## stat206 -1.463e-04 2.048e-04 -0.715 0.47495
## stat207 3.554e-04 2.026e-04 1.755 0.07936 .
## stat208 2.201e-04 2.042e-04 1.078 0.28123
## stat209 -1.502e-04 2.021e-04 -0.743 0.45728
## stat210 -1.467e-04 2.041e-04 -0.719 0.47234
## stat211 1.101e-07 2.027e-04 0.001 0.99957
## stat212 2.845e-05 2.031e-04 0.140 0.88858
## stat213 -2.865e-04 2.051e-04 -1.397 0.16260
## stat214 -1.736e-04 2.044e-04 -0.850 0.39563
## stat215 -1.955e-04 2.029e-04 -0.963 0.33537
## stat216 -1.771e-04 2.030e-04 -0.873 0.38293
## stat217 4.254e-04 2.042e-04 2.083 0.03726 *
## x18.sqrt 2.659e-02 7.772e-04 34.209 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02505 on 5055 degrees of freedom
## Multiple R-squared: 0.3739, Adjusted R-squared: 0.3442
## F-statistic: 12.58 on 240 and 5055 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 280"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# Checking to see if distributions are different and if so whcih variables
# High Leverage Plot
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,target=one_of(label.names))
ggplot(data=plotData, aes(x=type,y=target)) +
geom_boxplot(fill='light blue',outlier.shape=NA) +
scale_y_continuous(name="Target Variable Values",label=scales::comma_format(accuracy=.1)) +
theme_light() +
ggtitle('Distribution of High Leverage Points and Normal Points')
# 2 sample t-tests
plotData = data.train %>%
rownames_to_column() %>%
mutate(type=ifelse(rowname %in% high.cd,'High','Normal')) %>%
dplyr::select(type,one_of(feature.names))
comp.test = lapply(dplyr::select(plotData, one_of(feature.names))
, function(x) t.test(x ~ plotData$type, var.equal = TRUE))
sig.comp = list.filter(comp.test, p.value < 0.05)
sapply(sig.comp, function(x) x[['p.value']])## x13 stat19 stat85 stat98 stat110 stat128 stat146 stat151 stat170
## 3.359554e-02 2.259607e-02 2.327147e-02 8.755716e-06 3.281339e-04 2.242415e-04 3.912634e-02 1.276976e-02 3.055927e-02
## stat172 x18.sqrt
## 3.472633e-02 8.943334e-03mm = melt(plotData, id=c('type')) %>% filter(variable %in% names(sig.comp))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=5, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
# Distribution (box) Plots
mm = melt(plotData, id=c('type'))
ggplot(mm,aes(x=type, y=value)) +
geom_boxplot()+
facet_wrap(~variable, ncol=8, scales = 'free_y') +
scale_y_continuous(name="values",label=scales::comma_format(accuracy=.1)) +
ggtitle('Distribution of High Leverage Points and Normal Points')
Grand Means Model
model.null = lm(grand.mean.formula, data.train)
summary(model.null)##
## Call:
## lm(formula = grand.mean.formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.114992 -0.023860 -0.002993 0.020575 0.174910
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.0968675 0.0004808 4361 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03593 on 5583 degrees of freedomVariable Selection
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
Forward Selection with CV
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 11 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03389262 0.1107374 0.02638098 0.0006522431 0.01843699 0.0004657941
## 2 2 0.03307022 0.1535661 0.02570143 0.0007777253 0.02125833 0.0006093741
## 3 3 0.03251205 0.1824264 0.02515777 0.0007730663 0.02790904 0.0005946623
## 4 4 0.03203058 0.2063268 0.02453996 0.0007618678 0.02742323 0.0006125272
## 5 5 0.03175409 0.2198443 0.02433833 0.0007521550 0.02365268 0.0005893048
## 6 6 0.03164410 0.2252731 0.02426658 0.0007067374 0.02069752 0.0005718563
## 7 7 0.03167451 0.2237877 0.02430027 0.0007134016 0.02161979 0.0006044690
## 8 8 0.03162055 0.2265125 0.02428486 0.0007295711 0.02287693 0.0005987685
## 9 9 0.03155615 0.2297157 0.02422169 0.0007806923 0.02479613 0.0006297838
## 10 10 0.03155548 0.2298092 0.02421996 0.0007214398 0.02383271 0.0005854693
## 11 11 0.03154196 0.2304901 0.02420858 0.0007129736 0.02369648 0.0005638611
## 12 12 0.03157136 0.2290734 0.02422468 0.0007175387 0.02209994 0.0005662709
## 13 13 0.03157326 0.2289631 0.02424003 0.0006890899 0.02081163 0.0005325302
## 14 14 0.03157408 0.2288482 0.02424375 0.0006872834 0.02012904 0.0005257180
## 15 15 0.03156500 0.2293447 0.02422559 0.0007011488 0.02021158 0.0005422081
## 16 16 0.03156692 0.2292913 0.02421692 0.0007047558 0.01964155 0.0005341416
## 17 17 0.03157406 0.2290131 0.02421312 0.0007224985 0.01997446 0.0005265877
## 18 18 0.03156651 0.2293337 0.02420193 0.0007170687 0.01830741 0.0005263061
## 19 19 0.03154426 0.2304284 0.02418362 0.0007083238 0.01837859 0.0005279866
## 20 20 0.03156336 0.2295238 0.02420827 0.0007248759 0.01924171 0.0005474819
## 21 21 0.03159354 0.2281295 0.02422863 0.0007258288 0.02029223 0.0005583579
## 22 22 0.03158827 0.2284198 0.02423897 0.0007322096 0.02047236 0.0005712637
## 23 23 0.03158918 0.2284546 0.02422965 0.0007397660 0.02140798 0.0005825951
## 24 24 0.03156738 0.2294569 0.02421477 0.0007204914 0.02062076 0.0005591127
## 25 25 0.03158046 0.2288811 0.02424395 0.0007370698 0.01940678 0.0005602539
## 26 26 0.03156660 0.2296202 0.02424118 0.0007475190 0.02005125 0.0005655149
## 27 27 0.03157535 0.2292097 0.02425496 0.0007620121 0.02091631 0.0005994477
## 28 28 0.03157245 0.2293569 0.02425905 0.0007539778 0.02078355 0.0006000104
## 29 29 0.03157606 0.2292309 0.02427772 0.0007456688 0.02121314 0.0005949577
## 30 30 0.03158297 0.2289855 0.02427458 0.0007424941 0.02120135 0.0005905713
## 31 31 0.03159641 0.2284016 0.02427954 0.0007294122 0.02068815 0.0005790158
## 32 32 0.03162840 0.2269521 0.02430767 0.0007352183 0.02067730 0.0005812586
## 33 33 0.03163171 0.2269222 0.02431474 0.0007451232 0.02212524 0.0005848146
## 34 34 0.03165120 0.2260814 0.02433254 0.0007545036 0.02282494 0.0005976554
## 35 35 0.03165677 0.2257806 0.02433627 0.0007670402 0.02282972 0.0006149066
## 36 36 0.03165992 0.2256477 0.02433483 0.0007757491 0.02300518 0.0006239556
## 37 37 0.03166073 0.2256000 0.02433813 0.0007776993 0.02251088 0.0006295498
## 38 38 0.03169350 0.2241666 0.02437638 0.0007785527 0.02202197 0.0006242243
## 39 39 0.03170841 0.2234815 0.02438115 0.0007746087 0.02145523 0.0006218006
## 40 40 0.03172080 0.2229621 0.02438731 0.0007762988 0.02190566 0.0006237509
## 41 41 0.03171933 0.2230222 0.02438021 0.0007870144 0.02199319 0.0006318247
## 42 42 0.03173215 0.2224369 0.02438865 0.0007887085 0.02184682 0.0006332416
## 43 43 0.03173805 0.2221917 0.02439324 0.0007844157 0.02225580 0.0006386062
## 44 44 0.03174866 0.2217454 0.02439946 0.0007925515 0.02205424 0.0006406263
## 45 45 0.03175382 0.2215894 0.02441245 0.0007919993 0.02228831 0.0006324808
## 46 46 0.03176008 0.2213054 0.02441978 0.0008012386 0.02215076 0.0006444014
## 47 47 0.03177571 0.2206776 0.02442649 0.0008048797 0.02241642 0.0006426561
## 48 48 0.03178057 0.2204795 0.02443155 0.0007964909 0.02258343 0.0006338613
## 49 49 0.03179672 0.2197388 0.02443360 0.0007995788 0.02267451 0.0006244367
## 50 50 0.03181036 0.2191674 0.02445138 0.0007983631 0.02292363 0.0006280739
## 51 51 0.03183012 0.2182995 0.02445626 0.0007799544 0.02233104 0.0006117159
## 52 52 0.03184665 0.2176371 0.02447949 0.0007916784 0.02267022 0.0006194747
## 53 53 0.03187557 0.2163804 0.02450370 0.0007910934 0.02222590 0.0006221402
## 54 54 0.03188452 0.2160411 0.02450243 0.0007948626 0.02260704 0.0006285390
## 55 55 0.03190424 0.2151724 0.02451560 0.0007967573 0.02274345 0.0006338123
## 56 56 0.03191153 0.2148899 0.02452341 0.0007871291 0.02235004 0.0006410270
## 57 57 0.03192564 0.2142624 0.02452632 0.0007792204 0.02183397 0.0006373998
## 58 58 0.03193314 0.2139404 0.02452961 0.0007865110 0.02187050 0.0006531216
## 59 59 0.03195015 0.2131738 0.02454439 0.0007753268 0.02163585 0.0006557963
## 60 60 0.03195640 0.2129078 0.02454641 0.0007774081 0.02152700 0.0006510219
## 61 61 0.03196346 0.2126280 0.02454408 0.0007752047 0.02150169 0.0006492815
## 62 62 0.03197592 0.2121158 0.02455345 0.0007787450 0.02153486 0.0006472016
## 63 63 0.03197501 0.2121812 0.02455545 0.0007837428 0.02211224 0.0006522922
## 64 64 0.03197631 0.2121295 0.02455476 0.0007854134 0.02220941 0.0006528830
## 65 65 0.03197725 0.2120342 0.02455636 0.0007788172 0.02182623 0.0006393144
## 66 66 0.03197269 0.2122167 0.02456108 0.0007740063 0.02169081 0.0006406713
## 67 67 0.03198506 0.2116904 0.02456877 0.0007839419 0.02211752 0.0006520579
## 68 68 0.03199413 0.2112616 0.02458253 0.0007859389 0.02239952 0.0006499410
## 69 69 0.03199373 0.2113137 0.02457883 0.0007798220 0.02205815 0.0006385058
## 70 70 0.03199677 0.2112019 0.02457828 0.0007698666 0.02177686 0.0006251077
## 71 71 0.03199485 0.2113026 0.02458069 0.0007730486 0.02175998 0.0006162567
## 72 72 0.03200907 0.2107239 0.02458530 0.0007669151 0.02173014 0.0006092107
## 73 73 0.03200855 0.2107544 0.02459189 0.0007757266 0.02215077 0.0006122265
## 74 74 0.03201117 0.2106437 0.02459826 0.0007800256 0.02242840 0.0006149851
## 75 75 0.03201431 0.2105191 0.02460003 0.0007845042 0.02257636 0.0006234061
## 76 76 0.03201160 0.2106621 0.02460640 0.0007867395 0.02262212 0.0006221411
## 77 77 0.03201266 0.2106268 0.02460864 0.0007886349 0.02265895 0.0006271847
## 78 78 0.03202110 0.2102683 0.02460766 0.0007773304 0.02259104 0.0006266930
## 79 79 0.03202476 0.2101262 0.02461330 0.0007777689 0.02258518 0.0006284273
## 80 80 0.03202903 0.2099449 0.02461587 0.0007674038 0.02217838 0.0006157880
## 81 81 0.03203439 0.2097460 0.02461984 0.0007694261 0.02247091 0.0006160833
## 82 82 0.03203382 0.2097776 0.02462296 0.0007794749 0.02305641 0.0006279420
## 83 83 0.03204315 0.2093723 0.02463137 0.0007730535 0.02275154 0.0006261352
## 84 84 0.03204357 0.2093814 0.02462948 0.0007692575 0.02281881 0.0006261303
## 85 85 0.03203773 0.2096284 0.02462763 0.0007668067 0.02279669 0.0006276699
## 86 86 0.03203401 0.2097795 0.02462317 0.0007593516 0.02250249 0.0006268781
## 87 87 0.03204387 0.2093783 0.02463290 0.0007672806 0.02266784 0.0006240430
## 88 88 0.03203691 0.2096838 0.02462673 0.0007756540 0.02282587 0.0006247119
## 89 89 0.03204180 0.2094776 0.02462968 0.0007624696 0.02266256 0.0006148940
## 90 90 0.03205013 0.2091577 0.02463574 0.0007552168 0.02248753 0.0006034368
## 91 91 0.03204325 0.2094303 0.02463652 0.0007551801 0.02249424 0.0006064418
## 92 92 0.03204110 0.2095022 0.02463821 0.0007564882 0.02269060 0.0006096217
## 93 93 0.03204804 0.2091832 0.02464576 0.0007642170 0.02263359 0.0006153836
## 94 94 0.03205150 0.2090376 0.02465272 0.0007614395 0.02282187 0.0006116581
## 95 95 0.03205771 0.2087716 0.02466657 0.0007685122 0.02292044 0.0006146102
## 96 96 0.03206383 0.2085595 0.02467353 0.0007704949 0.02286605 0.0006184227
## 97 97 0.03207374 0.2081871 0.02467893 0.0007669434 0.02296847 0.0006139094
## 98 98 0.03206930 0.2083985 0.02467383 0.0007598021 0.02256854 0.0006110285
## 99 99 0.03206030 0.2087952 0.02466112 0.0007621025 0.02276911 0.0006118157
## 100 100 0.03206239 0.2087650 0.02466531 0.0007631129 0.02287832 0.0006166457
## 101 101 0.03206401 0.2086989 0.02466818 0.0007695363 0.02327026 0.0006213793
## 102 102 0.03206894 0.2085221 0.02467414 0.0007649475 0.02340219 0.0006172890
## 103 103 0.03206915 0.2084901 0.02467590 0.0007673951 0.02338727 0.0006181730
## 104 104 0.03207108 0.2084366 0.02467206 0.0007713758 0.02359671 0.0006210283
## 105 105 0.03206698 0.2086246 0.02467290 0.0007651343 0.02360692 0.0006239227
## 106 106 0.03207714 0.2081655 0.02468269 0.0007701618 0.02334966 0.0006278058
## 107 107 0.03207889 0.2081224 0.02468436 0.0007700058 0.02322265 0.0006331312
## 108 108 0.03208110 0.2080548 0.02468898 0.0007715476 0.02330884 0.0006352272
## 109 109 0.03208564 0.2078974 0.02468895 0.0007688552 0.02350125 0.0006335068
## 110 110 0.03208484 0.2079583 0.02469073 0.0007684368 0.02358449 0.0006320604
## 111 111 0.03209115 0.2076804 0.02469429 0.0007641568 0.02359484 0.0006285761
## 112 112 0.03210008 0.2072880 0.02469761 0.0007561856 0.02346173 0.0006254599
## 113 113 0.03210582 0.2070602 0.02469876 0.0007538455 0.02351254 0.0006296495
## 114 114 0.03211036 0.2068609 0.02470260 0.0007508418 0.02332469 0.0006273500
## 115 115 0.03211472 0.2066601 0.02470800 0.0007480500 0.02327718 0.0006297465
## 116 116 0.03212181 0.2063789 0.02471166 0.0007585094 0.02373405 0.0006370484
## 117 117 0.03212937 0.2060703 0.02472076 0.0007564734 0.02385289 0.0006314804
## 118 118 0.03213464 0.2058998 0.02472557 0.0007585941 0.02417185 0.0006337082
## 119 119 0.03212276 0.2064290 0.02471104 0.0007574814 0.02427740 0.0006302112
## 120 120 0.03212236 0.2064681 0.02471002 0.0007543792 0.02424200 0.0006289935
## 121 121 0.03211955 0.2066522 0.02470603 0.0007491022 0.02428806 0.0006278584
## 122 122 0.03212870 0.2062503 0.02471278 0.0007494040 0.02425334 0.0006252750
## 123 123 0.03213217 0.2061358 0.02471091 0.0007524542 0.02455365 0.0006276453
## 124 124 0.03212654 0.2063931 0.02471048 0.0007617639 0.02466606 0.0006353973
## 125 125 0.03213110 0.2061848 0.02471517 0.0007597298 0.02465370 0.0006329262
## 126 126 0.03213655 0.2059573 0.02472117 0.0007567765 0.02454004 0.0006249616
## 127 127 0.03214156 0.2057590 0.02472606 0.0007571636 0.02442825 0.0006195472
## 128 128 0.03214168 0.2057691 0.02472654 0.0007544975 0.02463043 0.0006124497
## 129 129 0.03213917 0.2058760 0.02472679 0.0007578545 0.02479207 0.0006105473
## 130 130 0.03214027 0.2058703 0.02472381 0.0007589384 0.02477514 0.0006084672
## 131 131 0.03214948 0.2055264 0.02472998 0.0007602427 0.02493383 0.0006110121
## 132 132 0.03214754 0.2055897 0.02473569 0.0007564237 0.02486737 0.0006106477
## 133 133 0.03214923 0.2055522 0.02474112 0.0007509921 0.02463704 0.0006068702
## 134 134 0.03214591 0.2056965 0.02473626 0.0007521630 0.02477664 0.0006059703
## 135 135 0.03214476 0.2057035 0.02473412 0.0007506465 0.02478002 0.0006095934
## 136 136 0.03213873 0.2059317 0.02473443 0.0007521115 0.02446884 0.0006141233
## 137 137 0.03213892 0.2059276 0.02473378 0.0007433840 0.02420227 0.0006064884
## 138 138 0.03214101 0.2058565 0.02473078 0.0007358587 0.02392864 0.0005985141
## 139 139 0.03214038 0.2059084 0.02473152 0.0007380682 0.02401814 0.0006029309
## 140 140 0.03213963 0.2059209 0.02472860 0.0007366739 0.02412524 0.0006026217
## 141 141 0.03213712 0.2060562 0.02472461 0.0007408668 0.02416180 0.0006095230
## 142 142 0.03213206 0.2062776 0.02471759 0.0007470103 0.02438694 0.0006185876
## 143 143 0.03213143 0.2063054 0.02471905 0.0007427978 0.02407153 0.0006179216
## 144 144 0.03212694 0.2064889 0.02471576 0.0007437024 0.02426400 0.0006163579
## 145 145 0.03212649 0.2064974 0.02471591 0.0007421961 0.02415725 0.0006126216
## 146 146 0.03212387 0.2066081 0.02471277 0.0007484210 0.02392050 0.0006125326
## 147 147 0.03212841 0.2064177 0.02471639 0.0007536749 0.02413867 0.0006185756
## 148 148 0.03212876 0.2064184 0.02471613 0.0007501964 0.02419231 0.0006157088
## 149 149 0.03212223 0.2066948 0.02471618 0.0007470898 0.02430866 0.0006142094
## 150 150 0.03212757 0.2064647 0.02472051 0.0007449857 0.02420860 0.0006140338
## 151 151 0.03212061 0.2067597 0.02471559 0.0007439006 0.02430151 0.0006130492
## 152 152 0.03211941 0.2068092 0.02471305 0.0007487717 0.02448898 0.0006154598
## 153 153 0.03212053 0.2067751 0.02471206 0.0007479705 0.02432463 0.0006134153
## 154 154 0.03212253 0.2067065 0.02471682 0.0007460765 0.02417727 0.0006117524
## 155 155 0.03212490 0.2066088 0.02471968 0.0007462854 0.02404273 0.0006063273
## 156 156 0.03213089 0.2063489 0.02472253 0.0007436778 0.02386817 0.0006051497
## 157 157 0.03213119 0.2063593 0.02472286 0.0007451780 0.02410671 0.0006079654
## 158 158 0.03212722 0.2064945 0.02471998 0.0007391939 0.02380983 0.0006010202
## 159 159 0.03212709 0.2065100 0.02471618 0.0007364383 0.02384113 0.0006009256
## 160 160 0.03212378 0.2066799 0.02470548 0.0007309626 0.02377727 0.0005991584
## 161 161 0.03212690 0.2065313 0.02470692 0.0007280906 0.02353383 0.0005948796
## 162 162 0.03212607 0.2065556 0.02470793 0.0007243702 0.02338628 0.0005927453
## 163 163 0.03212730 0.2064982 0.02470824 0.0007214078 0.02335850 0.0005895246
## 164 164 0.03213011 0.2063875 0.02471193 0.0007152918 0.02318670 0.0005910299
## 165 165 0.03212962 0.2064030 0.02471428 0.0007210162 0.02322081 0.0005892562
## 166 166 0.03213054 0.2063542 0.02471802 0.0007210902 0.02309933 0.0005908111
## 167 167 0.03212708 0.2065094 0.02471525 0.0007151715 0.02283863 0.0005888532
## 168 168 0.03212814 0.2064668 0.02471721 0.0007213572 0.02311703 0.0005917779
## 169 169 0.03213288 0.2062512 0.02472036 0.0007247685 0.02317635 0.0005932638
## 170 170 0.03213220 0.2062923 0.02471969 0.0007222271 0.02315388 0.0005900226
## 171 171 0.03213426 0.2061920 0.02472193 0.0007259244 0.02309488 0.0005935151
## 172 172 0.03213216 0.2062855 0.02472161 0.0007279163 0.02313882 0.0005913237
## 173 173 0.03212780 0.2064950 0.02471934 0.0007276880 0.02319942 0.0005911671
## 174 174 0.03212592 0.2065835 0.02471966 0.0007269775 0.02337697 0.0005930050
## 175 175 0.03212919 0.2064497 0.02472361 0.0007288483 0.02349788 0.0005969331
## 176 176 0.03212498 0.2066179 0.02472028 0.0007300817 0.02359109 0.0005990690
## 177 177 0.03212447 0.2066279 0.02471997 0.0007328130 0.02357492 0.0005997371
## 178 178 0.03212460 0.2066435 0.02472257 0.0007308067 0.02353279 0.0005980228
## 179 179 0.03211966 0.2068668 0.02471943 0.0007344497 0.02365057 0.0005986615
## 180 180 0.03212345 0.2067046 0.02472209 0.0007317950 0.02354773 0.0005965431
## 181 181 0.03212416 0.2066744 0.02472113 0.0007332329 0.02374549 0.0005996148
## 182 182 0.03212624 0.2065701 0.02472119 0.0007329079 0.02355686 0.0006005722
## 183 183 0.03212291 0.2067106 0.02471790 0.0007355610 0.02354040 0.0006046783
## 184 184 0.03212163 0.2067514 0.02471943 0.0007370687 0.02368380 0.0006046984
## 185 185 0.03212317 0.2067045 0.02472064 0.0007375554 0.02374050 0.0006053190
## 186 186 0.03211928 0.2068657 0.02471635 0.0007408047 0.02372763 0.0006069212
## 187 187 0.03211922 0.2068702 0.02471649 0.0007414333 0.02383931 0.0006099567
## 188 188 0.03212219 0.2067518 0.02472037 0.0007390872 0.02387212 0.0006098114
## 189 189 0.03212454 0.2066545 0.02472041 0.0007402202 0.02392888 0.0006107112
## 190 190 0.03212149 0.2067808 0.02471847 0.0007440113 0.02398452 0.0006147095
## 191 191 0.03212298 0.2067257 0.02471771 0.0007442826 0.02398951 0.0006140418
## 192 192 0.03212279 0.2067393 0.02471832 0.0007429165 0.02397257 0.0006142717
## 193 193 0.03212049 0.2068400 0.02471873 0.0007441163 0.02400649 0.0006163243
## 194 194 0.03212257 0.2067607 0.02472049 0.0007404273 0.02386688 0.0006145488
## 195 195 0.03212131 0.2068183 0.02471917 0.0007376896 0.02387565 0.0006122051
## 196 196 0.03212031 0.2068688 0.02471681 0.0007417182 0.02390377 0.0006142890
## 197 197 0.03212045 0.2068753 0.02471452 0.0007437887 0.02397385 0.0006160127
## 198 198 0.03212154 0.2068258 0.02471709 0.0007421694 0.02393491 0.0006140363
## 199 199 0.03212072 0.2068682 0.02471544 0.0007386873 0.02389094 0.0006105555
## 200 200 0.03211858 0.2069697 0.02471151 0.0007426417 0.02403664 0.0006126826
## 201 201 0.03211790 0.2069942 0.02471179 0.0007397241 0.02392360 0.0006083483
## 202 202 0.03211893 0.2069400 0.02471175 0.0007401619 0.02392331 0.0006103416
## 203 203 0.03211760 0.2069927 0.02471003 0.0007419760 0.02393780 0.0006104905
## 204 204 0.03211518 0.2070880 0.02470971 0.0007467062 0.02406822 0.0006128792
## 205 205 0.03211361 0.2071597 0.02470897 0.0007446335 0.02391783 0.0006109022
## 206 206 0.03211671 0.2070267 0.02471071 0.0007447954 0.02393297 0.0006106550
## 207 207 0.03211887 0.2069371 0.02471254 0.0007427624 0.02402469 0.0006106533
## 208 208 0.03212148 0.2068280 0.02471433 0.0007421232 0.02403628 0.0006117620
## 209 209 0.03212021 0.2068822 0.02471515 0.0007409750 0.02398888 0.0006081807
## 210 210 0.03212055 0.2068709 0.02471569 0.0007407612 0.02400551 0.0006075216
## 211 211 0.03212133 0.2068386 0.02471700 0.0007418947 0.02403101 0.0006077557
## 212 212 0.03212200 0.2068115 0.02471718 0.0007436373 0.02408295 0.0006082503
## 213 213 0.03212086 0.2068608 0.02471562 0.0007435165 0.02402960 0.0006077945
## 214 214 0.03212133 0.2068388 0.02471609 0.0007441390 0.02405444 0.0006079927
## 215 215 0.03212246 0.2067857 0.02471634 0.0007449357 0.02405300 0.0006080494
## 216 216 0.03212350 0.2067373 0.02471743 0.0007426976 0.02393477 0.0006059977
## 217 217 0.03212368 0.2067302 0.02471694 0.0007412252 0.02386297 0.0006050774
## 218 218 0.03212379 0.2067215 0.02471769 0.0007408228 0.02386854 0.0006057193
## 219 219 0.03212279 0.2067716 0.02471636 0.0007421437 0.02393657 0.0006064402
## 220 220 0.03212450 0.2066997 0.02471782 0.0007426391 0.02400031 0.0006069893
## 221 221 0.03212575 0.2066443 0.02471894 0.0007413844 0.02395601 0.0006063551
## 222 222 0.03212639 0.2066166 0.02471963 0.0007421593 0.02398086 0.0006065577
## 223 223 0.03212626 0.2066201 0.02471904 0.0007423556 0.02394088 0.0006062469
## 224 224 0.03212560 0.2066442 0.02471841 0.0007430920 0.02393346 0.0006073315
## 225 225 0.03212529 0.2066575 0.02471795 0.0007423461 0.02394726 0.0006068688
## 226 226 0.03212681 0.2065956 0.02471927 0.0007429293 0.02398027 0.0006075466
## 227 227 0.03212656 0.2066043 0.02471878 0.0007427766 0.02396408 0.0006070635
## 228 228 0.03212623 0.2066188 0.02471921 0.0007426108 0.02396328 0.0006067486
## 229 229 0.03212581 0.2066407 0.02471867 0.0007424296 0.02396027 0.0006065668
## 230 230 0.03212592 0.2066317 0.02471903 0.0007418059 0.02392697 0.0006059406
## 231 231 0.03212575 0.2066382 0.02471866 0.0007418205 0.02392392 0.0006061647
## 232 232 0.03212581 0.2066364 0.02471837 0.0007410823 0.02389928 0.0006057639
## 233 233 0.03212556 0.2066484 0.02471830 0.0007413759 0.02390808 0.0006058601
## 234 234 0.03212530 0.2066589 0.02471809 0.0007407540 0.02389895 0.0006053082
## 235 235 0.03212532 0.2066565 0.02471804 0.0007406742 0.02389196 0.0006053883
## 236 236 0.03212554 0.2066474 0.02471826 0.0007406086 0.02388513 0.0006052655
## 237 237 0.03212572 0.2066387 0.02471830 0.0007405966 0.02388618 0.0006052283
## 238 238 0.03212562 0.2066425 0.02471821 0.0007407461 0.02389906 0.0006055257
## 239 239 0.03212566 0.2066410 0.02471819 0.0007407434 0.02389712 0.0006055051
## 240 240 0.03212568 0.2066400 0.02471817 0.0007406867 0.02389293 0.0006054287
## [1] "Best Model"
## nvmax
## 11 11
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 1.9943108240 1.987270e+00 2.001352e+00
## x4 -0.0000563195 -7.366668e-05 -3.897232e-05
## x7 0.0111695138 9.941573e-03 1.239745e-02
## x9 0.0032703436 2.633200e-03 3.907487e-03
## x10 0.0010757959 4.818071e-04 1.669785e-03
## x16 0.0009034675 4.932559e-04 1.313679e-03
## x17 0.0013944496 7.693954e-04 2.019504e-03
## x21 0.0001290356 4.794220e-05 2.101289e-04
## stat14 -0.0009237427 -1.396307e-03 -4.511779e-04
## stat98 0.0035049260 3.034519e-03 3.975332e-03
## stat110 -0.0031947718 -3.668557e-03 -2.720987e-03
## x18.sqrt 0.0265348474 2.470918e-02 2.836052e-02Test
if (algo.forward.caret == TRUE){
test.model(model=model.forward, test=data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.043 2.084 2.097 2.096 2.110 2.148
## [1] "leapForward Test MSE: 0.00103207531444324"
Backward Elimination with CV
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 11 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03389262 0.1107374 0.02638098 0.0006522431 0.01843699 0.0004657941
## 2 2 0.03307022 0.1535661 0.02570143 0.0007777253 0.02125833 0.0006093741
## 3 3 0.03251205 0.1824264 0.02515777 0.0007730663 0.02790904 0.0005946623
## 4 4 0.03203058 0.2063268 0.02453996 0.0007618678 0.02742323 0.0006125272
## 5 5 0.03175409 0.2198443 0.02433833 0.0007521550 0.02365268 0.0005893048
## 6 6 0.03164410 0.2252731 0.02426658 0.0007067374 0.02069752 0.0005718563
## 7 7 0.03167451 0.2237877 0.02430027 0.0007134016 0.02161979 0.0006044690
## 8 8 0.03162055 0.2265125 0.02428486 0.0007295711 0.02287693 0.0005987685
## 9 9 0.03155615 0.2297157 0.02422169 0.0007806923 0.02479613 0.0006297838
## 10 10 0.03155548 0.2298092 0.02421996 0.0007214398 0.02383271 0.0005854693
## 11 11 0.03154196 0.2304901 0.02420858 0.0007129736 0.02369648 0.0005638611
## 12 12 0.03157136 0.2290734 0.02422468 0.0007175387 0.02209994 0.0005662709
## 13 13 0.03157920 0.2286966 0.02424426 0.0006897733 0.02079344 0.0005319438
## 14 14 0.03159416 0.2279372 0.02426092 0.0006915752 0.02019683 0.0005240932
## 15 15 0.03157894 0.2287061 0.02423653 0.0007038994 0.02024370 0.0005411458
## 16 16 0.03156692 0.2292913 0.02421692 0.0007047558 0.01964155 0.0005341416
## 17 17 0.03157406 0.2290131 0.02421312 0.0007224985 0.01997446 0.0005265877
## 18 18 0.03156651 0.2293337 0.02420193 0.0007170687 0.01830741 0.0005263061
## 19 19 0.03154426 0.2304284 0.02418362 0.0007083238 0.01837859 0.0005279866
## 20 20 0.03155669 0.2298720 0.02419903 0.0007201011 0.01951147 0.0005360044
## 21 21 0.03159715 0.2279797 0.02422729 0.0007282979 0.02017570 0.0005567951
## 22 22 0.03158827 0.2284198 0.02423897 0.0007322096 0.02047236 0.0005712637
## 23 23 0.03158918 0.2284546 0.02422965 0.0007397660 0.02140798 0.0005825951
## 24 24 0.03156738 0.2294569 0.02421477 0.0007204914 0.02062076 0.0005591127
## 25 25 0.03157379 0.2291858 0.02423772 0.0007277905 0.01912965 0.0005541639
## 26 26 0.03156433 0.2297195 0.02423677 0.0007458641 0.02010390 0.0005630590
## 27 27 0.03157513 0.2292237 0.02425307 0.0007616370 0.02089499 0.0005961089
## 28 28 0.03157776 0.2290838 0.02425921 0.0007501304 0.02041643 0.0005949409
## 29 29 0.03158128 0.2290063 0.02427530 0.0007420975 0.02076487 0.0005906784
## 30 30 0.03159291 0.2285737 0.02428363 0.0007482834 0.02139915 0.0005913368
## 31 31 0.03160604 0.2279772 0.02428904 0.0007341778 0.02089710 0.0005808521
## 32 32 0.03162725 0.2270435 0.02430620 0.0007368468 0.02062860 0.0005822712
## 33 33 0.03162919 0.2270474 0.02431446 0.0007552904 0.02204605 0.0005883116
## 34 34 0.03164143 0.2264833 0.02433335 0.0007729105 0.02253207 0.0006026211
## 35 35 0.03165717 0.2257964 0.02434415 0.0007765375 0.02304420 0.0006267268
## 36 36 0.03167060 0.2252023 0.02434744 0.0007785353 0.02336139 0.0006252428
## 37 37 0.03166876 0.2252531 0.02435040 0.0007714393 0.02220022 0.0006194244
## 38 38 0.03169376 0.2241424 0.02437276 0.0007912063 0.02248597 0.0006410639
## 39 39 0.03170385 0.2236689 0.02437805 0.0007874504 0.02201962 0.0006413722
## 40 40 0.03171390 0.2232108 0.02438437 0.0007921855 0.02159826 0.0006371194
## 41 41 0.03171792 0.2229959 0.02438135 0.0007816881 0.02082254 0.0006325727
## 42 42 0.03172602 0.2226439 0.02438411 0.0007861808 0.02133991 0.0006323869
## 43 43 0.03172945 0.2225249 0.02438381 0.0007931064 0.02178236 0.0006463201
## 44 44 0.03174974 0.2216663 0.02439703 0.0007925777 0.02147923 0.0006406267
## 45 45 0.03175920 0.2213034 0.02440931 0.0007935219 0.02231360 0.0006444002
## 46 46 0.03176533 0.2210498 0.02441829 0.0008028667 0.02220946 0.0006492120
## 47 47 0.03177492 0.2206772 0.02441491 0.0008127269 0.02253869 0.0006471872
## 48 48 0.03178343 0.2203631 0.02442609 0.0008034322 0.02273128 0.0006364118
## 49 49 0.03179806 0.2196841 0.02443296 0.0007974818 0.02267730 0.0006249690
## 50 50 0.03181291 0.2190421 0.02444348 0.0007970046 0.02261601 0.0006342197
## 51 51 0.03182932 0.2183362 0.02445646 0.0007811276 0.02234062 0.0006116116
## 52 52 0.03184828 0.2175304 0.02447620 0.0007817739 0.02251523 0.0006112606
## 53 53 0.03185938 0.2170713 0.02448613 0.0007859098 0.02291475 0.0006230813
## 54 54 0.03187538 0.2164156 0.02449434 0.0007821842 0.02264840 0.0006216841
## 55 55 0.03189228 0.2156669 0.02450300 0.0007754059 0.02244418 0.0006314071
## 56 56 0.03190491 0.2151355 0.02450603 0.0007790697 0.02191727 0.0006367828
## 57 57 0.03192110 0.2144153 0.02451609 0.0007784437 0.02172463 0.0006371116
## 58 58 0.03193602 0.2137950 0.02452777 0.0007736859 0.02151472 0.0006432385
## 59 59 0.03194644 0.2133170 0.02453791 0.0007685173 0.02155852 0.0006449447
## 60 60 0.03195678 0.2128831 0.02454778 0.0007736210 0.02164678 0.0006509962
## 61 61 0.03195665 0.2128976 0.02454344 0.0007759470 0.02148315 0.0006597152
## 62 62 0.03197045 0.2123319 0.02455541 0.0007785415 0.02151578 0.0006558428
## 63 63 0.03197635 0.2121240 0.02456218 0.0007933063 0.02229882 0.0006684501
## 64 64 0.03198047 0.2119958 0.02456814 0.0007973936 0.02225452 0.0006689053
## 65 65 0.03199344 0.2114276 0.02457946 0.0008064336 0.02261372 0.0006686883
## 66 66 0.03198634 0.2117188 0.02457509 0.0008059377 0.02282986 0.0006667427
## 67 67 0.03197566 0.2121933 0.02456156 0.0008018230 0.02278480 0.0006678345
## 68 68 0.03198234 0.2119028 0.02457212 0.0007959841 0.02246759 0.0006645727
## 69 69 0.03197847 0.2120846 0.02456457 0.0007856155 0.02218130 0.0006546440
## 70 70 0.03198731 0.2116916 0.02456954 0.0007778978 0.02234026 0.0006425659
## 71 71 0.03199098 0.2115487 0.02456741 0.0007754980 0.02224916 0.0006340838
## 72 72 0.03199481 0.2114030 0.02456695 0.0007820242 0.02244035 0.0006338517
## 73 73 0.03200022 0.2111385 0.02457359 0.0007844170 0.02229295 0.0006374261
## 74 74 0.03200473 0.2108970 0.02458196 0.0007792156 0.02209528 0.0006330786
## 75 75 0.03200758 0.2108089 0.02459069 0.0007853012 0.02217727 0.0006356551
## 76 76 0.03200874 0.2107937 0.02459271 0.0007879390 0.02220519 0.0006312108
## 77 77 0.03202113 0.2102812 0.02460586 0.0007775727 0.02204681 0.0006287361
## 78 78 0.03201696 0.2104656 0.02459819 0.0007732127 0.02196829 0.0006172424
## 79 79 0.03201928 0.2104019 0.02460752 0.0007698698 0.02198916 0.0006129441
## 80 80 0.03203332 0.2098160 0.02462542 0.0007647552 0.02211553 0.0006068389
## 81 81 0.03203977 0.2095353 0.02462711 0.0007659991 0.02242300 0.0006130742
## 82 82 0.03204036 0.2095133 0.02462930 0.0007716606 0.02261209 0.0006110414
## 83 83 0.03203734 0.2096431 0.02462306 0.0007526437 0.02198310 0.0006038814
## 84 84 0.03203619 0.2097307 0.02462647 0.0007451801 0.02211496 0.0006016631
## 85 85 0.03203329 0.2098698 0.02462274 0.0007524970 0.02250258 0.0006099046
## 86 86 0.03203920 0.2096075 0.02463053 0.0007455977 0.02227444 0.0006032124
## 87 87 0.03203878 0.2096410 0.02462817 0.0007474677 0.02208991 0.0006073230
## 88 88 0.03203196 0.2099396 0.02461663 0.0007533145 0.02203955 0.0006097122
## 89 89 0.03203541 0.2098196 0.02461566 0.0007519211 0.02240207 0.0006139766
## 90 90 0.03203802 0.2097340 0.02461927 0.0007617944 0.02294072 0.0006213546
## 91 91 0.03203783 0.2096929 0.02461992 0.0007653889 0.02285103 0.0006246838
## 92 92 0.03204313 0.2094931 0.02462863 0.0007702754 0.02324702 0.0006248658
## 93 93 0.03205301 0.2090243 0.02464187 0.0007711120 0.02313184 0.0006295924
## 94 94 0.03205358 0.2090081 0.02464821 0.0007724452 0.02332751 0.0006224512
## 95 95 0.03206399 0.2085852 0.02465920 0.0007777621 0.02312808 0.0006188906
## 96 96 0.03207240 0.2082087 0.02467759 0.0007731283 0.02307798 0.0006201315
## 97 97 0.03207778 0.2080074 0.02468342 0.0007712514 0.02310149 0.0006301259
## 98 98 0.03207205 0.2082941 0.02467601 0.0007648914 0.02282054 0.0006240114
## 99 99 0.03205940 0.2088413 0.02466225 0.0007661558 0.02309161 0.0006186644
## 100 100 0.03206615 0.2086167 0.02467016 0.0007731032 0.02323021 0.0006230757
## 101 101 0.03206353 0.2087233 0.02466733 0.0007713341 0.02338976 0.0006229120
## 102 102 0.03206909 0.2084796 0.02467339 0.0007769378 0.02350300 0.0006249898
## 103 103 0.03207215 0.2083748 0.02467420 0.0007762447 0.02347047 0.0006254771
## 104 104 0.03207235 0.2083890 0.02467105 0.0007785150 0.02368898 0.0006274777
## 105 105 0.03207032 0.2085189 0.02467603 0.0007717164 0.02368532 0.0006267517
## 106 106 0.03207319 0.2083921 0.02467643 0.0007710330 0.02369136 0.0006304638
## 107 107 0.03207533 0.2082865 0.02468066 0.0007653860 0.02316499 0.0006285650
## 108 108 0.03208205 0.2080111 0.02468545 0.0007675703 0.02310296 0.0006307816
## 109 109 0.03208718 0.2078170 0.02468435 0.0007621884 0.02318517 0.0006268088
## 110 110 0.03208920 0.2077342 0.02468962 0.0007578775 0.02307552 0.0006199551
## 111 111 0.03209448 0.2074931 0.02468899 0.0007546370 0.02322106 0.0006192962
## 112 112 0.03210970 0.2068712 0.02470307 0.0007482211 0.02287796 0.0006160682
## 113 113 0.03211622 0.2065821 0.02471001 0.0007517131 0.02291154 0.0006201541
## 114 114 0.03211623 0.2065810 0.02470518 0.0007441282 0.02278149 0.0006139856
## 115 115 0.03212327 0.2062721 0.02471167 0.0007487726 0.02302943 0.0006191742
## 116 116 0.03212427 0.2062302 0.02471338 0.0007527897 0.02347782 0.0006226691
## 117 117 0.03212000 0.2064202 0.02470878 0.0007575358 0.02373485 0.0006239409
## 118 118 0.03212349 0.2062834 0.02470814 0.0007614702 0.02409342 0.0006308846
## 119 119 0.03212416 0.2063235 0.02470879 0.0007573635 0.02406495 0.0006285195
## 120 120 0.03212633 0.2063162 0.02471045 0.0007537083 0.02427215 0.0006312394
## 121 121 0.03212708 0.2063458 0.02470826 0.0007530308 0.02457510 0.0006335698
## 122 122 0.03213053 0.2061903 0.02471125 0.0007536489 0.02474979 0.0006368084
## 123 123 0.03212840 0.2063163 0.02470863 0.0007551720 0.02476922 0.0006390117
## 124 124 0.03213023 0.2062137 0.02470852 0.0007612437 0.02475869 0.0006408769
## 125 125 0.03212961 0.2062541 0.02470967 0.0007603137 0.02473905 0.0006314471
## 126 126 0.03213395 0.2060753 0.02471511 0.0007546082 0.02447199 0.0006222039
## 127 127 0.03213794 0.2059163 0.02471882 0.0007563696 0.02446492 0.0006160069
## 128 128 0.03214204 0.2057531 0.02472467 0.0007548106 0.02462856 0.0006102005
## 129 129 0.03214869 0.2054887 0.02473211 0.0007566135 0.02466626 0.0006112942
## 130 130 0.03215200 0.2053760 0.02473471 0.0007539712 0.02436234 0.0006070767
## 131 131 0.03214666 0.2056152 0.02473212 0.0007532039 0.02463221 0.0006069656
## 132 132 0.03214056 0.2058928 0.02472950 0.0007511681 0.02464673 0.0006033620
## 133 133 0.03214479 0.2057336 0.02473187 0.0007525865 0.02468217 0.0005992537
## 134 134 0.03214399 0.2057752 0.02472933 0.0007550070 0.02482559 0.0006038865
## 135 135 0.03214070 0.2058692 0.02472983 0.0007503584 0.02448372 0.0006028695
## 136 136 0.03214174 0.2058192 0.02472799 0.0007483078 0.02440672 0.0006020680
## 137 137 0.03213866 0.2059575 0.02472578 0.0007478554 0.02445742 0.0006095448
## 138 138 0.03213805 0.2059788 0.02472089 0.0007509237 0.02429070 0.0006145233
## 139 139 0.03213862 0.2059731 0.02472107 0.0007528934 0.02438591 0.0006198472
## 140 140 0.03213946 0.2059610 0.02472337 0.0007490287 0.02438826 0.0006152260
## 141 141 0.03213260 0.2062681 0.02471994 0.0007545629 0.02445408 0.0006146181
## 142 142 0.03212646 0.2064944 0.02471507 0.0007559026 0.02439785 0.0006180605
## 143 143 0.03212861 0.2064373 0.02471790 0.0007498941 0.02449906 0.0006173744
## 144 144 0.03212701 0.2065015 0.02471808 0.0007489096 0.02447890 0.0006155124
## 145 145 0.03213478 0.2061729 0.02472197 0.0007435217 0.02446492 0.0006138070
## 146 146 0.03212520 0.2065884 0.02471530 0.0007531535 0.02457787 0.0006153448
## 147 147 0.03212225 0.2067282 0.02471188 0.0007568609 0.02474961 0.0006153412
## 148 148 0.03212899 0.2064455 0.02471917 0.0007551678 0.02473385 0.0006149529
## 149 149 0.03212284 0.2067058 0.02471441 0.0007479597 0.02441619 0.0006117928
## 150 150 0.03212047 0.2068083 0.02471381 0.0007513471 0.02436591 0.0006167535
## 151 151 0.03212280 0.2066944 0.02471553 0.0007466749 0.02391460 0.0006126944
## 152 152 0.03212058 0.2067791 0.02471493 0.0007457267 0.02394567 0.0006114116
## 153 153 0.03212290 0.2066997 0.02471704 0.0007501140 0.02410400 0.0006117245
## 154 154 0.03212239 0.2067461 0.02471850 0.0007474402 0.02416470 0.0006100832
## 155 155 0.03212760 0.2065136 0.02472197 0.0007478692 0.02418024 0.0006061097
## 156 156 0.03212807 0.2064755 0.02472317 0.0007486285 0.02425454 0.0006086699
## 157 157 0.03212655 0.2065477 0.02472244 0.0007471831 0.02416878 0.0006058748
## 158 158 0.03212345 0.2066636 0.02472029 0.0007407456 0.02396676 0.0005999895
## 159 159 0.03212566 0.2065750 0.02471567 0.0007349433 0.02371918 0.0006002776
## 160 160 0.03212856 0.2064608 0.02471375 0.0007312474 0.02353107 0.0005942477
## 161 161 0.03213161 0.2063155 0.02471222 0.0007277384 0.02332216 0.0005950962
## 162 162 0.03213196 0.2062914 0.02471350 0.0007214554 0.02328260 0.0005936947
## 163 163 0.03213155 0.2063116 0.02470993 0.0007195561 0.02327293 0.0005914416
## 164 164 0.03212938 0.2064197 0.02471151 0.0007156952 0.02314973 0.0005941668
## 165 165 0.03212913 0.2064164 0.02471187 0.0007220093 0.02322512 0.0005935653
## 166 166 0.03212635 0.2065414 0.02471327 0.0007205078 0.02311760 0.0005937138
## 167 167 0.03212457 0.2066278 0.02471272 0.0007151061 0.02294933 0.0005898320
## 168 168 0.03212877 0.2064490 0.02471783 0.0007208881 0.02308536 0.0005912363
## 169 169 0.03213429 0.2061978 0.02472174 0.0007258654 0.02318296 0.0005939044
## 170 170 0.03213450 0.2062010 0.02472102 0.0007260212 0.02326413 0.0005912360
## 171 171 0.03213207 0.2063060 0.02471867 0.0007306272 0.02327237 0.0005952949
## 172 172 0.03213036 0.2063913 0.02471771 0.0007311588 0.02339356 0.0005987058
## 173 173 0.03212536 0.2066101 0.02471498 0.0007298911 0.02334140 0.0005988515
## 174 174 0.03212245 0.2067261 0.02471365 0.0007281729 0.02342527 0.0005965437
## 175 175 0.03212588 0.2065730 0.02471868 0.0007287127 0.02345189 0.0005973729
## 176 176 0.03212279 0.2067000 0.02471737 0.0007311018 0.02353952 0.0006008323
## 177 177 0.03212580 0.2065655 0.02472076 0.0007308040 0.02343405 0.0005979705
## 178 178 0.03212496 0.2066272 0.02472130 0.0007302567 0.02349599 0.0006008811
## 179 179 0.03212000 0.2068506 0.02471707 0.0007339362 0.02361414 0.0006039605
## 180 180 0.03212121 0.2068065 0.02471782 0.0007352219 0.02377820 0.0006061255
## 181 181 0.03212230 0.2067493 0.02471825 0.0007335405 0.02371664 0.0006042600
## 182 182 0.03212273 0.2067152 0.02471738 0.0007340286 0.02357375 0.0006052105
## 183 183 0.03211829 0.2068996 0.02471594 0.0007366371 0.02359309 0.0006052755
## 184 184 0.03211926 0.2068540 0.02471726 0.0007369368 0.02362409 0.0006071477
## 185 185 0.03212180 0.2067685 0.02472133 0.0007385147 0.02388042 0.0006075081
## 186 186 0.03212054 0.2068198 0.02471778 0.0007360012 0.02387130 0.0006061713
## 187 187 0.03212354 0.2067003 0.02472043 0.0007349509 0.02385099 0.0006079329
## 188 188 0.03212490 0.2066409 0.02472249 0.0007351593 0.02390753 0.0006086930
## 189 189 0.03212418 0.2066729 0.02472147 0.0007403160 0.02391592 0.0006099627
## 190 190 0.03212113 0.2067991 0.02471955 0.0007441045 0.02397148 0.0006139614
## 191 191 0.03212298 0.2067257 0.02471771 0.0007442826 0.02398951 0.0006140418
## 192 192 0.03212279 0.2067393 0.02471832 0.0007429165 0.02397257 0.0006142717
## 193 193 0.03212085 0.2068213 0.02471884 0.0007440543 0.02402189 0.0006163518
## 194 194 0.03212068 0.2068242 0.02471753 0.0007425872 0.02384035 0.0006153419
## 195 195 0.03211889 0.2069152 0.02471693 0.0007414865 0.02385030 0.0006132442
## 196 196 0.03211983 0.2068959 0.02471811 0.0007437939 0.02391511 0.0006130810
## 197 197 0.03211982 0.2069000 0.02471522 0.0007445346 0.02397707 0.0006153327
## 198 198 0.03212065 0.2068648 0.02471684 0.0007420407 0.02392757 0.0006132191
## 199 199 0.03212193 0.2068083 0.02471619 0.0007386708 0.02392176 0.0006104228
## 200 200 0.03211987 0.2069094 0.02471367 0.0007426967 0.02407062 0.0006131895
## 201 201 0.03211965 0.2069207 0.02471419 0.0007402789 0.02399496 0.0006093050
## 202 202 0.03212086 0.2068640 0.02471307 0.0007407145 0.02399400 0.0006106665
## 203 203 0.03211761 0.2069960 0.02470979 0.0007419990 0.02393238 0.0006100455
## 204 204 0.03211407 0.2071354 0.02470865 0.0007444526 0.02399015 0.0006109085
## 205 205 0.03211361 0.2071597 0.02470897 0.0007446335 0.02391783 0.0006109022
## 206 206 0.03211671 0.2070267 0.02471071 0.0007447954 0.02393297 0.0006106550
## 207 207 0.03211887 0.2069371 0.02471254 0.0007427624 0.02402469 0.0006106533
## 208 208 0.03212148 0.2068280 0.02471433 0.0007421232 0.02403628 0.0006117620
## 209 209 0.03212021 0.2068822 0.02471515 0.0007409750 0.02398888 0.0006081807
## 210 210 0.03212055 0.2068709 0.02471569 0.0007407612 0.02400551 0.0006075216
## 211 211 0.03212133 0.2068386 0.02471700 0.0007418947 0.02403101 0.0006077557
## 212 212 0.03212200 0.2068115 0.02471718 0.0007436373 0.02408295 0.0006082503
## 213 213 0.03212086 0.2068608 0.02471562 0.0007435165 0.02402960 0.0006077945
## 214 214 0.03212133 0.2068388 0.02471609 0.0007441390 0.02405444 0.0006079927
## 215 215 0.03212246 0.2067857 0.02471634 0.0007449357 0.02405300 0.0006080494
## 216 216 0.03212350 0.2067373 0.02471743 0.0007426976 0.02393477 0.0006059977
## 217 217 0.03212368 0.2067302 0.02471694 0.0007412252 0.02386297 0.0006050774
## 218 218 0.03212379 0.2067215 0.02471769 0.0007408228 0.02386854 0.0006057193
## 219 219 0.03212275 0.2067714 0.02471621 0.0007421308 0.02393664 0.0006064085
## 220 220 0.03212413 0.2067145 0.02471739 0.0007425265 0.02399580 0.0006068992
## 221 221 0.03212538 0.2066592 0.02471851 0.0007412701 0.02395142 0.0006062648
## 222 222 0.03212574 0.2066434 0.02471919 0.0007419616 0.02397252 0.0006064658
## 223 223 0.03212626 0.2066201 0.02471904 0.0007423556 0.02394088 0.0006062469
## 224 224 0.03212560 0.2066442 0.02471841 0.0007430920 0.02393346 0.0006073315
## 225 225 0.03212529 0.2066575 0.02471795 0.0007423461 0.02394726 0.0006068688
## 226 226 0.03212681 0.2065956 0.02471927 0.0007429293 0.02398027 0.0006075466
## 227 227 0.03212656 0.2066043 0.02471878 0.0007427766 0.02396408 0.0006070635
## 228 228 0.03212623 0.2066188 0.02471921 0.0007426108 0.02396328 0.0006067486
## 229 229 0.03212581 0.2066407 0.02471867 0.0007424296 0.02396027 0.0006065668
## 230 230 0.03212592 0.2066317 0.02471903 0.0007418059 0.02392697 0.0006059406
## 231 231 0.03212575 0.2066382 0.02471866 0.0007418205 0.02392392 0.0006061647
## 232 232 0.03212581 0.2066364 0.02471837 0.0007410823 0.02389928 0.0006057639
## 233 233 0.03212556 0.2066484 0.02471830 0.0007413759 0.02390808 0.0006058601
## 234 234 0.03212530 0.2066589 0.02471809 0.0007407540 0.02389895 0.0006053082
## 235 235 0.03212532 0.2066565 0.02471804 0.0007406742 0.02389196 0.0006053883
## 236 236 0.03212554 0.2066474 0.02471826 0.0007406086 0.02388513 0.0006052655
## 237 237 0.03212572 0.2066387 0.02471830 0.0007405966 0.02388618 0.0006052283
## 238 238 0.03212562 0.2066425 0.02471821 0.0007407461 0.02389906 0.0006055257
## 239 239 0.03212566 0.2066410 0.02471819 0.0007407434 0.02389712 0.0006055051
## 240 240 0.03212568 0.2066400 0.02471817 0.0007406867 0.02389293 0.0006054287
## [1] "Best Model"
## nvmax
## 11 11
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 1.9943108240 1.987270e+00 2.001352e+00
## x4 -0.0000563195 -7.366668e-05 -3.897232e-05
## x7 0.0111695138 9.941573e-03 1.239745e-02
## x9 0.0032703436 2.633200e-03 3.907487e-03
## x10 0.0010757959 4.818071e-04 1.669785e-03
## x16 0.0009034675 4.932559e-04 1.313679e-03
## x17 0.0013944496 7.693954e-04 2.019504e-03
## x21 0.0001290356 4.794220e-05 2.101289e-04
## stat14 -0.0009237427 -1.396307e-03 -4.511779e-04
## stat98 0.0035049260 3.034519e-03 3.975332e-03
## stat110 -0.0031947718 -3.668557e-03 -2.720987e-03
## x18.sqrt 0.0265348474 2.470918e-02 2.836052e-02Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.043 2.084 2.097 2.096 2.110 2.148
## [1] "leapBackward Test MSE: 0.00103207531444324"
Stepwise Selection with CV
Train
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 11 on full training set
## [1] "All models results"
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.03389262 0.1107374 0.02638098 0.0006522431 0.01843699 0.0004657941
## 2 2 0.03307022 0.1535661 0.02570143 0.0007777253 0.02125833 0.0006093741
## 3 3 0.03251205 0.1824264 0.02515777 0.0007730663 0.02790904 0.0005946623
## 4 4 0.03203058 0.2063268 0.02453996 0.0007618678 0.02742323 0.0006125272
## 5 5 0.03175409 0.2198443 0.02433833 0.0007521550 0.02365268 0.0005893048
## 6 6 0.03164410 0.2252731 0.02426658 0.0007067374 0.02069752 0.0005718563
## 7 7 0.03167451 0.2237877 0.02430027 0.0007134016 0.02161979 0.0006044690
## 8 8 0.03162055 0.2265125 0.02428486 0.0007295711 0.02287693 0.0005987685
## 9 9 0.03155615 0.2297157 0.02422169 0.0007806923 0.02479613 0.0006297838
## 10 10 0.03155548 0.2298092 0.02421996 0.0007214398 0.02383271 0.0005854693
## 11 11 0.03154196 0.2304901 0.02420858 0.0007129736 0.02369648 0.0005638611
## 12 12 0.03157136 0.2290734 0.02422468 0.0007175387 0.02209994 0.0005662709
## 13 13 0.03157326 0.2289631 0.02424003 0.0006890899 0.02081163 0.0005325302
## 14 14 0.03157408 0.2288482 0.02424375 0.0006872834 0.02012904 0.0005257180
## 15 15 0.03157894 0.2287061 0.02423653 0.0007038994 0.02024370 0.0005411458
## 16 16 0.03190636 0.2117547 0.02452156 0.0013404932 0.06017317 0.0011044116
## 17 17 0.03157406 0.2290131 0.02421312 0.0007224985 0.01997446 0.0005265877
## 18 18 0.03156651 0.2293337 0.02420193 0.0007170687 0.01830741 0.0005263061
## 19 19 0.03154426 0.2304284 0.02418362 0.0007083238 0.01837859 0.0005279866
## 20 20 0.03156336 0.2295238 0.02420827 0.0007248759 0.01924171 0.0005474819
## 21 21 0.03159715 0.2279797 0.02422729 0.0007282979 0.02017570 0.0005567951
## 22 22 0.03196738 0.2092553 0.02453578 0.0015485656 0.06013615 0.0012713111
## 23 23 0.03158918 0.2284546 0.02422965 0.0007397660 0.02140798 0.0005825951
## 24 24 0.03156738 0.2294569 0.02421477 0.0007204914 0.02062076 0.0005591127
## 25 25 0.03158046 0.2288811 0.02424395 0.0007370698 0.01940678 0.0005602539
## 26 26 0.03155988 0.2299272 0.02423487 0.0007381787 0.01977053 0.0005594708
## 27 27 0.03157513 0.2292237 0.02425307 0.0007616370 0.02089499 0.0005961089
## 28 28 0.03157278 0.2293200 0.02425732 0.0007545404 0.02083975 0.0005969809
## 29 29 0.03180893 0.2174105 0.02442729 0.0012809581 0.04991480 0.0009363540
## 30 30 0.03229356 0.1930513 0.02484382 0.0016910689 0.06879877 0.0013931207
## 31 31 0.03193126 0.2113926 0.02452373 0.0013507778 0.06042039 0.0010222070
## 32 32 0.03194276 0.2105584 0.02458709 0.0013168990 0.05826289 0.0010729542
## 33 33 0.03163171 0.2269222 0.02431474 0.0007451232 0.02212524 0.0005848146
## 34 34 0.03165120 0.2260814 0.02433254 0.0007545036 0.02282494 0.0005976554
## 35 35 0.03164835 0.2261771 0.02432278 0.0007779652 0.02291525 0.0006327695
## 36 36 0.03190482 0.2120608 0.02454376 0.0008175801 0.05080420 0.0008048053
## 37 37 0.03223647 0.1951826 0.02486195 0.0014064694 0.07066364 0.0011396934
## 38 38 0.03170411 0.2236700 0.02438520 0.0007675873 0.02116256 0.0006103664
## 39 39 0.03196900 0.2094742 0.02463244 0.0010131088 0.05118741 0.0008450926
## 40 40 0.03196216 0.2104704 0.02457026 0.0009346952 0.04384750 0.0007947740
## 41 41 0.03192549 0.2124119 0.02451896 0.0012361352 0.04679187 0.0009139803
## 42 42 0.03217811 0.2002617 0.02475941 0.0013738197 0.05953275 0.0010045000
## 43 43 0.03205242 0.2061287 0.02462206 0.0013589357 0.05964128 0.0010463279
## 44 44 0.03270386 0.1734083 0.02512338 0.0018333297 0.08130799 0.0013313729
## 45 45 0.03205640 0.2056472 0.02465931 0.0013004827 0.05601458 0.0010619360
## 46 46 0.03221936 0.1985616 0.02479355 0.0013553883 0.05856631 0.0009874377
## 47 47 0.03177494 0.2206460 0.02442074 0.0008064939 0.02222634 0.0006460526
## 48 48 0.03202344 0.2077207 0.02462188 0.0009752004 0.04581255 0.0008351891
## 49 49 0.03296207 0.1595841 0.02538980 0.0017383653 0.07823696 0.0013980231
## 50 50 0.03204341 0.2060375 0.02463894 0.0007839917 0.04815828 0.0007573110
## 51 51 0.03206358 0.2051349 0.02464930 0.0007638784 0.04789335 0.0007449423
## 52 52 0.03184275 0.2178206 0.02447732 0.0007952133 0.02297393 0.0006213095
## 53 53 0.03218564 0.2006009 0.02474453 0.0011034122 0.04444579 0.0008989274
## 54 54 0.03272897 0.1719717 0.02525041 0.0016035335 0.07328474 0.0012624810
## 55 55 0.03190696 0.2150266 0.02450950 0.0007919428 0.02295894 0.0006465792
## 56 56 0.03234443 0.1933654 0.02487484 0.0013027446 0.05620578 0.0009719069
## 57 57 0.03190826 0.2150342 0.02450711 0.0007731364 0.02170786 0.0006391728
## 58 58 0.03270840 0.1728509 0.02522079 0.0011853066 0.06469140 0.0010109080
## 59 59 0.03216460 0.2007868 0.02471767 0.0007355282 0.04601677 0.0007522352
## 60 60 0.03258182 0.1810157 0.02504379 0.0017598213 0.07367551 0.0014331603
## 61 61 0.03217749 0.2002409 0.02472311 0.0007516287 0.04654581 0.0007534026
## 62 62 0.03270112 0.1723941 0.02518733 0.0012381587 0.07342228 0.0010739223
## 63 63 0.03303636 0.1566573 0.02536752 0.0017599415 0.07813027 0.0014057263
## 64 64 0.03198178 0.2118771 0.02456126 0.0007936143 0.02250020 0.0006583984
## 65 65 0.03227865 0.1966534 0.02481696 0.0014181398 0.05569133 0.0011230864
## 66 66 0.03225265 0.1977175 0.02477948 0.0012661378 0.05455858 0.0009811456
## 67 67 0.03228552 0.1963687 0.02482691 0.0014201821 0.05564907 0.0011313731
## 68 68 0.03239186 0.1889456 0.02486805 0.0011488409 0.05940391 0.0009812912
## 69 69 0.03292106 0.1641962 0.02532547 0.0018663962 0.07439338 0.0015179714
## 70 70 0.03228190 0.1965133 0.02482179 0.0014066723 0.05535723 0.0011032126
## 71 71 0.03242249 0.1869698 0.02498789 0.0008577006 0.05900046 0.0008312052
## 72 72 0.03263117 0.1791488 0.02509048 0.0018208783 0.07199665 0.0014550252
## 73 73 0.03226859 0.1970791 0.02479467 0.0012548538 0.05441653 0.0009492339
## 74 74 0.03254785 0.1819450 0.02502171 0.0009745416 0.05587756 0.0009345276
## 75 75 0.03264442 0.1782365 0.02509928 0.0017374921 0.07186230 0.0014153600
## 76 76 0.03253261 0.1825747 0.02503149 0.0013337934 0.06604520 0.0011417823
## 77 77 0.03227804 0.1966769 0.02480360 0.0012537172 0.05433758 0.0009701228
## 78 78 0.03286111 0.1664006 0.02529508 0.0014125608 0.06860469 0.0011823598
## 79 79 0.03232460 0.1948419 0.02484955 0.0010716578 0.04348243 0.0008891385
## 80 80 0.03299645 0.1604910 0.02543018 0.0016574642 0.07354738 0.0012389834
## 81 81 0.03203145 0.2098580 0.02462138 0.0007695140 0.02243368 0.0006214841
## 82 82 0.03224029 0.1980646 0.02484341 0.0009336145 0.04602808 0.0007666668
## 83 83 0.03223523 0.1989800 0.02476874 0.0011971892 0.04715206 0.0009132621
## 84 84 0.03277294 0.1728990 0.02521700 0.0013303382 0.05919834 0.0009641456
## 85 85 0.03281866 0.1710558 0.02523939 0.0016711046 0.06877583 0.0012488075
## 86 86 0.03249750 0.1845183 0.02503379 0.0012801992 0.06427935 0.0010009530
## 87 87 0.03280002 0.1714870 0.02524755 0.0015214516 0.06847507 0.0011245466
## 88 88 0.03233594 0.1943903 0.02487820 0.0013793063 0.05447681 0.0010849318
## 89 89 0.03222450 0.1995041 0.02475916 0.0012002133 0.04772528 0.0009190266
## 90 90 0.03254352 0.1826926 0.02510358 0.0014340406 0.06510248 0.0011255931
## 91 91 0.03238513 0.1924834 0.02489125 0.0014818651 0.05697926 0.0011954186
## 92 92 0.03224006 0.1981625 0.02485293 0.0009259335 0.04623628 0.0007592645
## 93 93 0.03204973 0.2091133 0.02464788 0.0007630802 0.02266234 0.0006141097
## 94 94 0.03257437 0.1809023 0.02509379 0.0013011009 0.06567833 0.0011195969
## 95 95 0.03206123 0.2086692 0.02466295 0.0007724915 0.02299611 0.0006223798
## 96 96 0.03331895 0.1422237 0.02571213 0.0019243695 0.08460243 0.0015018316
## 97 97 0.03261531 0.1797927 0.02509662 0.0011951369 0.05910872 0.0010101957
## 98 98 0.03281894 0.1708758 0.02529712 0.0015227201 0.06837044 0.0011294593
## 99 99 0.03259488 0.1807404 0.02512520 0.0015255755 0.06668401 0.0012239505
## 100 100 0.03250003 0.1872431 0.02501616 0.0012202174 0.05246380 0.0008259194
## 101 101 0.03238220 0.1924862 0.02491359 0.0011120299 0.04670515 0.0009208317
## 102 102 0.03207302 0.2083361 0.02467570 0.0007658074 0.02330937 0.0006177188
## 103 103 0.03251042 0.1868173 0.02502162 0.0012198557 0.05247733 0.0008104407
## 104 104 0.03235978 0.1936575 0.02491642 0.0013618990 0.05396057 0.0010680689
## 105 105 0.03239992 0.1921270 0.02492509 0.0014720671 0.05693844 0.0011912118
## 106 106 0.03208365 0.2079157 0.02468668 0.0007690143 0.02360825 0.0006302179
## 107 107 0.03272777 0.1748933 0.02519339 0.0012914664 0.06361111 0.0009158302
## 108 108 0.03256879 0.1823655 0.02508556 0.0016432724 0.06728165 0.0012813883
## 109 109 0.03208839 0.2077815 0.02468660 0.0007638979 0.02321952 0.0006291254
## 110 110 0.03275143 0.1742155 0.02524319 0.0014720328 0.06578984 0.0012417361
## 111 111 0.03210022 0.2072567 0.02469912 0.0007532593 0.02329091 0.0006201568
## 112 112 0.03234495 0.1934208 0.02488906 0.0007455030 0.04916116 0.0007782915
## 113 113 0.03282220 0.1682226 0.02531206 0.0013679681 0.07386064 0.0011005833
## 114 114 0.03278215 0.1729357 0.02525850 0.0014818603 0.06615637 0.0012516033
## 115 115 0.03282348 0.1687880 0.02525418 0.0016128246 0.07653423 0.0012973311
## 116 116 0.03297523 0.1617093 0.02537799 0.0015938689 0.07732054 0.0013721641
## 117 117 0.03266643 0.1781347 0.02517356 0.0016298579 0.07095424 0.0013324249
## 118 118 0.03240974 0.1916885 0.02495676 0.0013292524 0.05280513 0.0010497223
## 119 119 0.03261332 0.1802813 0.02511146 0.0014298646 0.06552485 0.0011537237
## 120 120 0.03229448 0.1967973 0.02490154 0.0008657819 0.04189151 0.0007341068
## 121 121 0.03227531 0.1978130 0.02482283 0.0008834765 0.04170865 0.0007578720
## 122 122 0.03234726 0.1942724 0.02489595 0.0007634031 0.04729228 0.0007926131
## 123 123 0.03239991 0.1926545 0.02498390 0.0009662668 0.03903177 0.0009746519
## 124 124 0.03263165 0.1805597 0.02509780 0.0010689266 0.04606071 0.0007422657
## 125 125 0.03284427 0.1695182 0.02529752 0.0015538037 0.06662734 0.0013126628
## 126 126 0.03243223 0.1911956 0.02493885 0.0008845017 0.03451720 0.0005518075
## 127 127 0.03213794 0.2059163 0.02471882 0.0007563696 0.02446492 0.0006160069
## 128 128 0.03240114 0.1923913 0.02497495 0.0011193227 0.04702881 0.0009758222
## 129 129 0.03214064 0.2057934 0.02472525 0.0007576194 0.02471343 0.0006083244
## 130 130 0.03234329 0.1953112 0.02489857 0.0012666434 0.05064304 0.0010301210
## 131 131 0.03215423 0.2053147 0.02473458 0.0007625378 0.02500559 0.0006138360
## 132 132 0.03236292 0.1947478 0.02494170 0.0008428065 0.03130747 0.0007882416
## 133 133 0.03246571 0.1880965 0.02499406 0.0008095321 0.05050795 0.0007927231
## 134 134 0.03234827 0.1951122 0.02491964 0.0009961354 0.04021427 0.0008235674
## 135 135 0.03214651 0.2056296 0.02473753 0.0007550915 0.02504273 0.0006088901
## 136 136 0.03250483 0.1867763 0.02501774 0.0012122568 0.05062705 0.0009244021
## 137 137 0.03272336 0.1755202 0.02518225 0.0008100232 0.04594793 0.0006543020
## 138 138 0.03286597 0.1680172 0.02534444 0.0013508950 0.05540468 0.0011132573
## 139 139 0.03213980 0.2059246 0.02472159 0.0007383313 0.02408760 0.0006088668
## 140 140 0.03279876 0.1723497 0.02522430 0.0010439499 0.04878411 0.0008361220
## 141 141 0.03228084 0.1980190 0.02485333 0.0008434060 0.03881870 0.0006539497
## 142 142 0.03231800 0.1962194 0.02488409 0.0007288258 0.04264854 0.0007560841
## 143 143 0.03231249 0.1964752 0.02487780 0.0007265343 0.04253209 0.0007564128
## 144 144 0.03250434 0.1870728 0.02498109 0.0012564309 0.05271093 0.0010187274
## 145 145 0.03246186 0.1882370 0.02501522 0.0007800813 0.05030780 0.0007485211
## 146 146 0.03228614 0.1980761 0.02483963 0.0009421280 0.03782737 0.0007582706
## 147 147 0.03212439 0.2066283 0.02471155 0.0007572386 0.02475593 0.0006200199
## 148 148 0.03279512 0.1727491 0.02526594 0.0013497432 0.05228611 0.0011412622
## 149 149 0.03212233 0.2067047 0.02471583 0.0007487306 0.02448356 0.0006148482
## 150 150 0.03238229 0.1939010 0.02490365 0.0007968104 0.02864210 0.0004684423
## 151 151 0.03275673 0.1744202 0.02523422 0.0012607549 0.05258216 0.0010422328
## 152 152 0.03236674 0.1945862 0.02488977 0.0007960599 0.02826401 0.0004687335
## 153 153 0.03261601 0.1823983 0.02506313 0.0011971036 0.04331338 0.0008337506
## 154 154 0.03273379 0.1753356 0.02524099 0.0011649759 0.04947155 0.0010052775
## 155 155 0.03212747 0.2065048 0.02471961 0.0007451542 0.02409970 0.0006054221
## 156 156 0.03230235 0.1973791 0.02485826 0.0009664567 0.03912220 0.0007777554
## 157 157 0.03227549 0.1983409 0.02485214 0.0008436627 0.03881141 0.0006468913
## 158 158 0.03285877 0.1682981 0.02535308 0.0012703161 0.05658262 0.0011175112
## 159 159 0.03244966 0.1894975 0.02496935 0.0010867507 0.04703700 0.0008743687
## 160 160 0.03230124 0.1974384 0.02484859 0.0009581915 0.03913552 0.0007714527
## 161 161 0.03258283 0.1833713 0.02507221 0.0006930945 0.04231538 0.0005990178
## 162 162 0.03237783 0.1942782 0.02488930 0.0012257032 0.04492003 0.0009677082
## 163 163 0.03229270 0.1977343 0.02483510 0.0008638382 0.04052628 0.0007397562
## 164 164 0.03213083 0.2063660 0.02471082 0.0007154935 0.02319874 0.0005939863
## 165 165 0.03229131 0.1977951 0.02483823 0.0008661526 0.04053791 0.0007432873
## 166 166 0.03212787 0.2064684 0.02471457 0.0007220392 0.02311780 0.0005953232
## 167 167 0.03236467 0.1946424 0.02492524 0.0008838034 0.03421602 0.0008231460
## 168 168 0.03254317 0.1855407 0.02502903 0.0012894299 0.05395799 0.0010496752
## 169 169 0.03238119 0.1939853 0.02490309 0.0007779993 0.02780307 0.0004557753
## 170 170 0.03213389 0.2062221 0.02471898 0.0007266104 0.02328550 0.0005914244
## 171 171 0.03230372 0.1974000 0.02485292 0.0010141597 0.03631847 0.0007877086
## 172 172 0.03213171 0.2063021 0.02472116 0.0007275140 0.02313804 0.0005910438
## 173 173 0.03212436 0.2066456 0.02471346 0.0007305029 0.02332999 0.0005987271
## 174 174 0.03236115 0.1948452 0.02492836 0.0008823393 0.03377038 0.0008177006
## 175 175 0.03212588 0.2065730 0.02471868 0.0007287127 0.02345189 0.0005973729
## 176 176 0.03230320 0.1973545 0.02486245 0.0009675710 0.03941914 0.0007817729
## 177 177 0.03233930 0.1955725 0.02490764 0.0007389759 0.04430253 0.0007780034
## 178 178 0.03212460 0.2066435 0.02472257 0.0007308067 0.02353279 0.0005980228
## 179 179 0.03211966 0.2068668 0.02471943 0.0007344497 0.02365057 0.0005986615
## 180 180 0.03212345 0.2067046 0.02472209 0.0007317950 0.02354773 0.0005965431
## 181 181 0.03227059 0.1986670 0.02484626 0.0008333514 0.03838499 0.0006473446
## 182 182 0.03212549 0.2066035 0.02471853 0.0007340489 0.02363249 0.0006065225
## 183 183 0.03212182 0.2067590 0.02471665 0.0007372081 0.02365035 0.0006074755
## 184 184 0.03228411 0.1983258 0.02487134 0.0011314842 0.04350718 0.0009678256
## 185 185 0.03231140 0.1968470 0.02489048 0.0009759886 0.03877548 0.0008057550
## 186 186 0.03261688 0.1826699 0.02507366 0.0012117376 0.04338476 0.0008449042
## 187 187 0.03212354 0.2067003 0.02472043 0.0007349509 0.02385099 0.0006079329
## 188 188 0.03271750 0.1760710 0.02524236 0.0010796804 0.04977342 0.0009309751
## 189 189 0.03212454 0.2066545 0.02472041 0.0007402202 0.02392888 0.0006107112
## 190 190 0.03237661 0.1941804 0.02494091 0.0009262456 0.03585763 0.0008543306
## 191 191 0.03227252 0.1986018 0.02484862 0.0008484927 0.03888484 0.0006611327
## 192 192 0.03212279 0.2067393 0.02471832 0.0007429165 0.02397257 0.0006142717
## 193 193 0.03212049 0.2068400 0.02471873 0.0007441163 0.02400649 0.0006163243
## 194 194 0.03236386 0.1948409 0.02489572 0.0007700140 0.02684707 0.0004516523
## 195 195 0.03254624 0.1853773 0.02507973 0.0009996753 0.04662736 0.0009464343
## 196 196 0.03211866 0.2069436 0.02471517 0.0007440972 0.02388126 0.0006151766
## 197 197 0.03212030 0.2068781 0.02471536 0.0007446741 0.02398357 0.0006153619
## 198 198 0.03212070 0.2068622 0.02471730 0.0007420512 0.02392750 0.0006132222
## 199 199 0.03254132 0.1855151 0.02507159 0.0009709762 0.05386286 0.0009242990
## 200 200 0.03247202 0.1883849 0.02502590 0.0010534061 0.04898955 0.0008330219
## 201 201 0.03231617 0.1969197 0.02486917 0.0010106702 0.04147785 0.0008086191
## 202 202 0.03212045 0.2068743 0.02471308 0.0007398835 0.02397711 0.0006106790
## 203 203 0.03229894 0.1976979 0.02485596 0.0009101831 0.04240294 0.0007931080
## 204 204 0.03211407 0.2071354 0.02470865 0.0007444526 0.02399015 0.0006109085
## 205 205 0.03229148 0.1981582 0.02487531 0.0011880177 0.04578411 0.0010150249
## 206 206 0.03211671 0.2070267 0.02471071 0.0007447954 0.02393297 0.0006106550
## 207 207 0.03211887 0.2069371 0.02471254 0.0007427624 0.02402469 0.0006106533
## 208 208 0.03261720 0.1824213 0.02511071 0.0008691547 0.03283763 0.0006916846
## 209 209 0.03212021 0.2068822 0.02471515 0.0007409750 0.02398888 0.0006081807
## 210 210 0.03212055 0.2068709 0.02471569 0.0007407612 0.02400551 0.0006075216
## 211 211 0.03212133 0.2068386 0.02471700 0.0007418947 0.02403101 0.0006077557
## 212 212 0.03231318 0.1968899 0.02488291 0.0009903616 0.03938384 0.0008081808
## 213 213 0.03212086 0.2068608 0.02471562 0.0007435165 0.02402960 0.0006077945
## 214 214 0.03212133 0.2068388 0.02471609 0.0007441390 0.02405444 0.0006079927
## 215 215 0.03268063 0.1801816 0.02516311 0.0014002530 0.05227637 0.0011752653
## 216 216 0.03230009 0.1976550 0.02485208 0.0010396276 0.03742624 0.0008042829
## 217 217 0.03212368 0.2067302 0.02471694 0.0007412252 0.02386297 0.0006050774
## 218 218 0.03212379 0.2067215 0.02471769 0.0007408228 0.02386854 0.0006057193
## 219 219 0.03212279 0.2067716 0.02471636 0.0007421437 0.02393657 0.0006064402
## 220 220 0.03239850 0.1934103 0.02495784 0.0009593283 0.03735062 0.0008821692
## 221 221 0.03212575 0.2066443 0.02471894 0.0007413844 0.02395601 0.0006063551
## 222 222 0.03255048 0.1851097 0.02508822 0.0009753751 0.05303685 0.0009280365
## 223 223 0.03233454 0.1962169 0.02489273 0.0010401791 0.04259350 0.0008456203
## 224 224 0.03258596 0.1843012 0.02507020 0.0014725559 0.05340019 0.0011604255
## 225 225 0.03212529 0.2066575 0.02471795 0.0007423461 0.02394726 0.0006068688
## 226 226 0.03233024 0.1963998 0.02488963 0.0010301119 0.04208109 0.0008380879
## 227 227 0.03230123 0.1975935 0.02487127 0.0008882659 0.04111235 0.0006762506
## 228 228 0.03237485 0.1943663 0.02489854 0.0007866438 0.02791711 0.0004657703
## 229 229 0.03212581 0.2066407 0.02471867 0.0007424296 0.02396027 0.0006065668
## 230 230 0.03233011 0.1962688 0.02489453 0.0010210913 0.04062813 0.0008329102
## 231 231 0.03232256 0.1967568 0.02487605 0.0009375355 0.04385260 0.0008125199
## 232 232 0.03254075 0.1857811 0.02502507 0.0010065551 0.03596151 0.0006477208
## 233 233 0.03232399 0.1968593 0.02490264 0.0012425605 0.04796890 0.0010621841
## 234 234 0.03212530 0.2066589 0.02471809 0.0007407540 0.02389895 0.0006053082
## 235 235 0.03242393 0.1928416 0.02495409 0.0013546307 0.04903128 0.0011069195
## 236 236 0.03246543 0.1890727 0.02499402 0.0010984918 0.04737600 0.0008141455
## 237 237 0.03271168 0.1773100 0.02522445 0.0015345402 0.05998383 0.0012653944
## 238 238 0.03271903 0.1767379 0.02522470 0.0012565159 0.05810254 0.0009799755
## 239 239 0.03336489 0.1468546 0.02575478 0.0013820283 0.06609633 0.0013056925
## 240 240 0.03212568 0.2066400 0.02471817 0.0007406867 0.02389293 0.0006054287
## [1] "Best Model"
## nvmax
## 11 11
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients of final model:"
## Estimate 2.5 % 97.5 %
## (Intercept) 1.9943108240 1.987270e+00 2.001352e+00
## x4 -0.0000563195 -7.366668e-05 -3.897232e-05
## x7 0.0111695138 9.941573e-03 1.239745e-02
## x9 0.0032703436 2.633200e-03 3.907487e-03
## x10 0.0010757959 4.818071e-04 1.669785e-03
## x16 0.0009034675 4.932559e-04 1.313679e-03
## x17 0.0013944496 7.693954e-04 2.019504e-03
## x21 0.0001290356 4.794220e-05 2.101289e-04
## stat14 -0.0009237427 -1.396307e-03 -4.511779e-04
## stat98 0.0035049260 3.034519e-03 3.975332e-03
## stat110 -0.0031947718 -3.668557e-03 -2.720987e-03
## x18.sqrt 0.0265348474 2.470918e-02 2.836052e-02Test
if (algo.stepwise.caret == TRUE){
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.043 2.084 2.097 2.096 2.110 2.148
## [1] "leapSeq Test MSE: 0.00103207531444324"
LASSO with CV
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
tune.grid= expand.grid(alpha = 1,lambda = 10^seq(from=-4,to=-2,length=100))
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,tune.grid = tune.grid
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.000614 on full training set
## glmnet
##
## 5584 samples
## 240 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0001000000 0.03190271 0.2144654 0.02454145
## 0.0001047616 0.03189414 0.2147859 0.02453422
## 0.0001097499 0.03188531 0.2151179 0.02452686
## 0.0001149757 0.03187622 0.2154622 0.02451931
## 0.0001204504 0.03186676 0.2158236 0.02451148
## 0.0001261857 0.03185709 0.2161949 0.02450344
## 0.0001321941 0.03184721 0.2165771 0.02449534
## 0.0001384886 0.03183712 0.2169699 0.02448693
## 0.0001450829 0.03182696 0.2173687 0.02447837
## 0.0001519911 0.03181655 0.2177801 0.02446977
## 0.0001592283 0.03180604 0.2181990 0.02446146
## 0.0001668101 0.03179535 0.2186288 0.02445289
## 0.0001747528 0.03178447 0.2190708 0.02444400
## 0.0001830738 0.03177341 0.2195248 0.02443501
## 0.0001917910 0.03176203 0.2199978 0.02442575
## 0.0002009233 0.03175067 0.2204744 0.02441655
## 0.0002104904 0.03173947 0.2209480 0.02440763
## 0.0002205131 0.03172845 0.2214188 0.02439873
## 0.0002310130 0.03171753 0.2218896 0.02439019
## 0.0002420128 0.03170655 0.2223700 0.02438152
## 0.0002535364 0.03169503 0.2228824 0.02437206
## 0.0002656088 0.03168359 0.2233993 0.02436297
## 0.0002782559 0.03167175 0.2239435 0.02435399
## 0.0002915053 0.03165993 0.2244965 0.02434518
## 0.0003053856 0.03164790 0.2250702 0.02433642
## 0.0003199267 0.03163595 0.2256510 0.02432782
## 0.0003351603 0.03162372 0.2262581 0.02431946
## 0.0003511192 0.03161185 0.2268593 0.02431165
## 0.0003678380 0.03160042 0.2274520 0.02430444
## 0.0003853529 0.03158955 0.2280282 0.02429743
## 0.0004037017 0.03157914 0.2285932 0.02429046
## 0.0004229243 0.03156909 0.2291560 0.02428446
## 0.0004430621 0.03155981 0.2296966 0.02427874
## 0.0004641589 0.03155088 0.2302360 0.02427359
## 0.0004862602 0.03154251 0.2307611 0.02426926
## 0.0005094138 0.03153514 0.2312513 0.02426557
## 0.0005336699 0.03152928 0.2316796 0.02426285
## 0.0005590810 0.03152484 0.2320525 0.02426129
## 0.0005857021 0.03152315 0.2323010 0.02426204
## 0.0006135907 0.03152309 0.2324790 0.02426444
## 0.0006428073 0.03152603 0.2325134 0.02426905
## 0.0006734151 0.03153079 0.2324693 0.02427491
## 0.0007054802 0.03153794 0.2323141 0.02428215
## 0.0007390722 0.03154677 0.2320882 0.02429079
## 0.0007742637 0.03155851 0.2317254 0.02430201
## 0.0008111308 0.03157185 0.2312972 0.02431494
## 0.0008497534 0.03158686 0.2308023 0.02432953
## 0.0008902151 0.03160319 0.2302556 0.02434514
## 0.0009326033 0.03161901 0.2297603 0.02436121
## 0.0009770100 0.03163637 0.2292050 0.02437886
## 0.0010235310 0.03165402 0.2286602 0.02439776
## 0.0010722672 0.03167316 0.2280605 0.02441787
## 0.0011233240 0.03169253 0.2274738 0.02443760
## 0.0011768120 0.03171390 0.2268037 0.02445868
## 0.0012328467 0.03173476 0.2261932 0.02447971
## 0.0012915497 0.03175766 0.2255052 0.02450238
## 0.0013530478 0.03178113 0.2248254 0.02452564
## 0.0014174742 0.03180668 0.2240677 0.02455081
## 0.0014849683 0.03183380 0.2232641 0.02457694
## 0.0015556761 0.03186237 0.2224327 0.02460443
## 0.0016297508 0.03189074 0.2216815 0.02463169
## 0.0017073526 0.03192077 0.2209023 0.02466095
## 0.0017886495 0.03194999 0.2202524 0.02469058
## 0.0018738174 0.03198168 0.2195332 0.02472253
## 0.0019630407 0.03201446 0.2188311 0.02475566
## 0.0020565123 0.03205047 0.2180254 0.02479145
## 0.0021544347 0.03208984 0.2171126 0.02483014
## 0.0022570197 0.03213299 0.2160683 0.02487160
## 0.0023644894 0.03217959 0.2149148 0.02491568
## 0.0024770764 0.03222991 0.2136380 0.02496258
## 0.0025950242 0.03228033 0.2124913 0.02500946
## 0.0027185882 0.03233433 0.2112550 0.02505870
## 0.0028480359 0.03239065 0.2100386 0.02510947
## 0.0029836472 0.03245226 0.2086208 0.02516456
## 0.0031257158 0.03251962 0.2069640 0.02522339
## 0.0032745492 0.03259339 0.2050144 0.02528687
## 0.0034304693 0.03267417 0.2027112 0.02535527
## 0.0035938137 0.03276241 0.1999937 0.02542901
## 0.0037649358 0.03285823 0.1968194 0.02550791
## 0.0039442061 0.03296073 0.1932161 0.02559150
## 0.0041320124 0.03306246 0.1897863 0.02567445
## 0.0043287613 0.03317054 0.1859806 0.02576127
## 0.0045348785 0.03327979 0.1822245 0.02584869
## 0.0047508102 0.03339911 0.1776468 0.02594242
## 0.0049770236 0.03352944 0.1720322 0.02604573
## 0.0052140083 0.03367061 0.1652223 0.02615737
## 0.0054622772 0.03381699 0.1576297 0.02627107
## 0.0057223677 0.03396547 0.1495244 0.02638473
## 0.0059948425 0.03409635 0.1430791 0.02648246
## 0.0062802914 0.03423105 0.1360314 0.02658196
## 0.0065793322 0.03434908 0.1307364 0.02666487
## 0.0068926121 0.03447498 0.1243557 0.02675270
## 0.0072208090 0.03459904 0.1178950 0.02683823
## 0.0075646333 0.03471948 0.1117274 0.02692217
## 0.0079248290 0.03480372 0.1111523 0.02697830
## 0.0083021757 0.03489409 0.1107374 0.02703862
## 0.0086974900 0.03499020 0.1107374 0.02710390
## 0.0091116276 0.03509537 0.1107374 0.02717632
## 0.0095454846 0.03521043 0.1107374 0.02725612
## 0.0100000000 0.03533629 0.1107374 0.02734383
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.0006135907.
## alpha lambda
## 40 1 0.0006135907
## alpha lambda RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 0.0001000000 0.03190271 0.2144654 0.02454145 0.0007394030 0.02350810 0.0006117962
## 2 1 0.0001047616 0.03189414 0.2147859 0.02453422 0.0007394684 0.02350126 0.0006121414
## 3 1 0.0001097499 0.03188531 0.2151179 0.02452686 0.0007394897 0.02349322 0.0006122428
## 4 1 0.0001149757 0.03187622 0.2154622 0.02451931 0.0007394557 0.02348266 0.0006121873
## 5 1 0.0001204504 0.03186676 0.2158236 0.02451148 0.0007392446 0.02346629 0.0006119792
## 6 1 0.0001261857 0.03185709 0.2161949 0.02450344 0.0007390227 0.02344593 0.0006117518
## 7 1 0.0001321941 0.03184721 0.2165771 0.02449534 0.0007389286 0.02342324 0.0006115184
## 8 1 0.0001384886 0.03183712 0.2169699 0.02448693 0.0007388938 0.02340211 0.0006113427
## 9 1 0.0001450829 0.03182696 0.2173687 0.02447837 0.0007390322 0.02338713 0.0006112145
## 10 1 0.0001519911 0.03181655 0.2177801 0.02446977 0.0007390960 0.02336916 0.0006111745
## 11 1 0.0001592283 0.03180604 0.2181990 0.02446146 0.0007393279 0.02335158 0.0006112963
## 12 1 0.0001668101 0.03179535 0.2186288 0.02445289 0.0007395850 0.02333438 0.0006114187
## 13 1 0.0001747528 0.03178447 0.2190708 0.02444400 0.0007399694 0.02331901 0.0006119651
## 14 1 0.0001830738 0.03177341 0.2195248 0.02443501 0.0007404217 0.02330706 0.0006125844
## 15 1 0.0001917910 0.03176203 0.2199978 0.02442575 0.0007410064 0.02329542 0.0006132019
## 16 1 0.0002009233 0.03175067 0.2204744 0.02441655 0.0007416469 0.02328080 0.0006137531
## 17 1 0.0002104904 0.03173947 0.2209480 0.02440763 0.0007424796 0.02326645 0.0006147318
## 18 1 0.0002205131 0.03172845 0.2214188 0.02439873 0.0007431696 0.02323892 0.0006156781
## 19 1 0.0002310130 0.03171753 0.2218896 0.02439019 0.0007434228 0.02318963 0.0006161595
## 20 1 0.0002420128 0.03170655 0.2223700 0.02438152 0.0007435908 0.02313947 0.0006164338
## 21 1 0.0002535364 0.03169503 0.2228824 0.02437206 0.0007434450 0.02307306 0.0006159699
## 22 1 0.0002656088 0.03168359 0.2233993 0.02436297 0.0007433120 0.02300229 0.0006152005
## 23 1 0.0002782559 0.03167175 0.2239435 0.02435399 0.0007428041 0.02290590 0.0006139342
## 24 1 0.0002915053 0.03165993 0.2244965 0.02434518 0.0007424213 0.02281559 0.0006126886
## 25 1 0.0003053856 0.03164790 0.2250702 0.02433642 0.0007421332 0.02272601 0.0006113223
## 26 1 0.0003199267 0.03163595 0.2256510 0.02432782 0.0007419496 0.02265130 0.0006101811
## 27 1 0.0003351603 0.03162372 0.2262581 0.02431946 0.0007418650 0.02258680 0.0006090833
## 28 1 0.0003511192 0.03161185 0.2268593 0.02431165 0.0007419187 0.02252997 0.0006079242
## 29 1 0.0003678380 0.03160042 0.2274520 0.02430444 0.0007420205 0.02248746 0.0006066079
## 30 1 0.0003853529 0.03158955 0.2280282 0.02429743 0.0007422441 0.02244443 0.0006051530
## 31 1 0.0004037017 0.03157914 0.2285932 0.02429046 0.0007420263 0.02238922 0.0006031878
## 32 1 0.0004229243 0.03156909 0.2291560 0.02428446 0.0007420057 0.02235483 0.0006014143
## 33 1 0.0004430621 0.03155981 0.2296966 0.02427874 0.0007418582 0.02234123 0.0005989639
## 34 1 0.0004641589 0.03155088 0.2302360 0.02427359 0.0007417976 0.02234701 0.0005964558
## 35 1 0.0004862602 0.03154251 0.2307611 0.02426926 0.0007411469 0.02236224 0.0005939990
## 36 1 0.0005094138 0.03153514 0.2312513 0.02426557 0.0007402845 0.02236592 0.0005909291
## 37 1 0.0005336699 0.03152928 0.2316796 0.02426285 0.0007387387 0.02235211 0.0005879360
## 38 1 0.0005590810 0.03152484 0.2320525 0.02426129 0.0007369529 0.02231904 0.0005847095
## 39 1 0.0005857021 0.03152315 0.2323010 0.02426204 0.0007343731 0.02229532 0.0005814910
## 40 1 0.0006135907 0.03152309 0.2324790 0.02426444 0.0007318168 0.02225113 0.0005785909
## 41 1 0.0006428073 0.03152603 0.2325134 0.02426905 0.0007296733 0.02222789 0.0005757620
## 42 1 0.0006734151 0.03153079 0.2324693 0.02427491 0.0007277034 0.02219165 0.0005730695
## 43 1 0.0007054802 0.03153794 0.2323141 0.02428215 0.0007263464 0.02216967 0.0005710969
## 44 1 0.0007390722 0.03154677 0.2320882 0.02429079 0.0007254756 0.02217516 0.0005689687
## 45 1 0.0007742637 0.03155851 0.2317254 0.02430201 0.0007250007 0.02224684 0.0005675354
## 46 1 0.0008111308 0.03157185 0.2312972 0.02431494 0.0007249360 0.02235860 0.0005663985
## 47 1 0.0008497534 0.03158686 0.2308023 0.02432953 0.0007251667 0.02253413 0.0005653006
## 48 1 0.0008902151 0.03160319 0.2302556 0.02434514 0.0007250196 0.02273754 0.0005639068
## 49 1 0.0009326033 0.03161901 0.2297603 0.02436121 0.0007249412 0.02289676 0.0005627742
## 50 1 0.0009770100 0.03163637 0.2292050 0.02437886 0.0007250968 0.02308603 0.0005619073
## 51 1 0.0010235310 0.03165402 0.2286602 0.02439776 0.0007247242 0.02323280 0.0005606970
## 52 1 0.0010722672 0.03167316 0.2280605 0.02441787 0.0007245577 0.02342046 0.0005598561
## 53 1 0.0011233240 0.03169253 0.2274738 0.02443760 0.0007247053 0.02360544 0.0005591817
## 54 1 0.0011768120 0.03171390 0.2268037 0.02445868 0.0007244583 0.02377651 0.0005580432
## 55 1 0.0012328467 0.03173476 0.2261932 0.02447971 0.0007243583 0.02386430 0.0005566820
## 56 1 0.0012915497 0.03175766 0.2255052 0.02450238 0.0007241455 0.02394754 0.0005554957
## 57 1 0.0013530478 0.03178113 0.2248254 0.02452564 0.0007230493 0.02394228 0.0005545058
## 58 1 0.0014174742 0.03180668 0.2240677 0.02455081 0.0007213968 0.02392449 0.0005522177
## 59 1 0.0014849683 0.03183380 0.2232641 0.02457694 0.0007191405 0.02386439 0.0005496581
## 60 1 0.0015556761 0.03186237 0.2224327 0.02460443 0.0007167096 0.02388080 0.0005466460
## 61 1 0.0016297508 0.03189074 0.2216815 0.02463169 0.0007140884 0.02393707 0.0005427227
## 62 1 0.0017073526 0.03192077 0.2209023 0.02466095 0.0007119097 0.02409880 0.0005389978
## 63 1 0.0017886495 0.03194999 0.2202524 0.02469058 0.0007112454 0.02431390 0.0005363139
## 64 1 0.0018738174 0.03198168 0.2195332 0.02472253 0.0007106754 0.02455921 0.0005339988
## 65 1 0.0019630407 0.03201446 0.2188311 0.02475566 0.0007100052 0.02478785 0.0005318817
## 66 1 0.0020565123 0.03205047 0.2180254 0.02479145 0.0007094207 0.02503483 0.0005305832
## 67 1 0.0021544347 0.03208984 0.2171126 0.02483014 0.0007090416 0.02530282 0.0005299464
## 68 1 0.0022570197 0.03213299 0.2160683 0.02487160 0.0007085130 0.02557737 0.0005291116
## 69 1 0.0023644894 0.03217959 0.2149148 0.02491568 0.0007073644 0.02581593 0.0005279470
## 70 1 0.0024770764 0.03222991 0.2136380 0.02496258 0.0007057550 0.02606126 0.0005260746
## 71 1 0.0025950242 0.03228033 0.2124913 0.02500946 0.0007024218 0.02607484 0.0005230471
## 72 1 0.0027185882 0.03233433 0.2112550 0.02505870 0.0006988856 0.02615426 0.0005206359
## 73 1 0.0028480359 0.03239065 0.2100386 0.02510947 0.0006959879 0.02626721 0.0005194000
## 74 1 0.0029836472 0.03245226 0.2086208 0.02516456 0.0006929834 0.02638031 0.0005179562
## 75 1 0.0031257158 0.03251962 0.2069640 0.02522339 0.0006898757 0.02649501 0.0005164134
## 76 1 0.0032745492 0.03259339 0.2050144 0.02528687 0.0006866039 0.02660342 0.0005148057
## 77 1 0.0034304693 0.03267417 0.2027112 0.02535527 0.0006831627 0.02670063 0.0005132502
## 78 1 0.0035938137 0.03276241 0.1999937 0.02542901 0.0006797825 0.02676901 0.0005114157
## 79 1 0.0037649358 0.03285823 0.1968194 0.02550791 0.0006771743 0.02675908 0.0005093543
## 80 1 0.0039442061 0.03296073 0.1932161 0.02559150 0.0006749052 0.02668983 0.0005074250
## 81 1 0.0041320124 0.03306246 0.1897863 0.02567445 0.0006744275 0.02603599 0.0005081192
## 82 1 0.0043287613 0.03317054 0.1859806 0.02576127 0.0006735030 0.02560924 0.0005079720
## 83 1 0.0045348785 0.03327979 0.1822245 0.02584869 0.0006721281 0.02516915 0.0005073799
## 84 1 0.0047508102 0.03339911 0.1776468 0.02594242 0.0006711143 0.02465790 0.0005067750
## 85 1 0.0049770236 0.03352944 0.1720322 0.02604573 0.0006704727 0.02405735 0.0005066270
## 86 1 0.0052140083 0.03367061 0.1652223 0.02615737 0.0006698979 0.02331575 0.0005049030
## 87 1 0.0054622772 0.03381699 0.1576297 0.02627107 0.0006684952 0.02188436 0.0005037608
## 88 1 0.0057223677 0.03396547 0.1495244 0.02638473 0.0006659512 0.02146618 0.0005014981
## 89 1 0.0059948425 0.03409635 0.1430791 0.02648246 0.0006642036 0.02083604 0.0004970764
## 90 1 0.0062802914 0.03423105 0.1360314 0.02658196 0.0006604601 0.02104041 0.0004913022
## 91 1 0.0065793322 0.03434908 0.1307364 0.02666487 0.0006569373 0.02032876 0.0004868250
## 92 1 0.0068926121 0.03447498 0.1243557 0.02675270 0.0006528054 0.01997225 0.0004809552
## 93 1 0.0072208090 0.03459904 0.1178950 0.02683823 0.0006521126 0.01873740 0.0004784223
## 94 1 0.0075646333 0.03471948 0.1117274 0.02692217 0.0006498951 0.01913629 0.0004765770
## 95 1 0.0079248290 0.03480372 0.1111523 0.02697830 0.0006548050 0.01863348 0.0004791280
## 96 1 0.0083021757 0.03489409 0.1107374 0.02703862 0.0006591118 0.01843699 0.0004813476
## 97 1 0.0086974900 0.03499020 0.1107374 0.02710390 0.0006627005 0.01843699 0.0004833738
## 98 1 0.0091116276 0.03509537 0.1107374 0.02717632 0.0006667329 0.01843699 0.0004850861
## 99 1 0.0095454846 0.03521043 0.1107374 0.02725612 0.0006712469 0.01843699 0.0004855545
## 100 1 0.0100000000 0.03533629 0.1107374 0.02734383 0.0006762820 0.01843699 0.0004856660
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## model.coef
## (Intercept) 1.998342e+00
## x4 -4.287751e-05
## x7 1.021217e-02
## x8 2.103332e-04
## x9 2.779636e-03
## x10 6.234475e-04
## x11 6.509776e+04
## x14 -2.941676e-05
## x16 5.864226e-04
## x17 9.365317e-04
## x21 7.116198e-05
## stat3 1.047522e-06
## stat4 -2.735986e-04
## stat5 -1.000693e-04
## stat13 -2.315316e-04
## stat14 -5.723076e-04
## stat23 2.539117e-04
## stat24 -2.215479e-04
## stat25 -1.175249e-04
## stat26 -4.756610e-05
## stat35 -6.700945e-05
## stat37 -1.275452e-04
## stat41 -2.940955e-04
## stat43 -3.979572e-05
## stat51 9.289780e-06
## stat54 -4.758027e-05
## stat59 1.661202e-04
## stat60 6.644573e-05
## stat91 -1.781202e-04
## stat98 3.150897e-03
## stat100 3.834476e-04
## stat103 -2.181209e-05
## stat104 -7.016582e-05
## stat106 -4.220241e-06
## stat110 -2.865590e-03
## stat114 4.268180e-07
## stat131 5.979429e-05
## stat144 7.032314e-05
## stat146 -1.292041e-04
## stat149 -3.490215e-04
## stat156 2.325891e-04
## stat195 4.356156e-05
## stat202 -1.376595e-05
## stat204 -2.832993e-04
## stat214 -2.233937e-05
## stat217 1.721133e-04
## x18.sqrt 2.511251e-02Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.049 2.084 2.097 2.096 2.109 2.140
## [1] "glmnet LASSO Test MSE: 0.00103788978157203"
LARS with CV
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, : There were missing values in resampled
## performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.374 on full training set
## Least Angle Regression
##
## 5584 samples
## 240 predictor
##
## Pre-processing: centered (240), scaled (240)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5026, 5026, 5026, 5025, 5025, 5026, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 0.03592121 NaN 0.02775138
## 0.01010101 0.03549321 0.1107374 0.02745325
## 0.02020202 0.03511281 0.1107374 0.02718792
## 0.03030303 0.03478158 0.1107374 0.02696330
## 0.04040404 0.03449727 0.1233921 0.02676654
## 0.05050505 0.03424128 0.1356525 0.02658789
## 0.06060606 0.03400785 0.1473743 0.02641609
## 0.07070707 0.03378802 0.1590250 0.02624775
## 0.08080808 0.03357686 0.1699324 0.02608249
## 0.09090909 0.03337762 0.1785918 0.02592585
## 0.10101010 0.03319129 0.1853278 0.02577822
## 0.11111111 0.03302282 0.1910499 0.02564264
## 0.12121212 0.03286544 0.1964940 0.02551420
## 0.13131313 0.03271417 0.2014549 0.02538945
## 0.14141414 0.03257330 0.2055040 0.02527056
## 0.15151515 0.03244319 0.2087738 0.02515765
## 0.16161616 0.03232543 0.2113825 0.02505197
## 0.17171717 0.03222011 0.2138857 0.02495486
## 0.18181818 0.03212280 0.2162374 0.02486280
## 0.19191919 0.03203363 0.2183239 0.02477575
## 0.20202020 0.03195776 0.2199931 0.02469900
## 0.21212121 0.03189107 0.2216240 0.02463328
## 0.22222222 0.03183040 0.2233642 0.02457488
## 0.23232323 0.03177907 0.2248948 0.02452489
## 0.24242424 0.03173865 0.2260772 0.02448394
## 0.25252525 0.03170389 0.2271076 0.02444847
## 0.26262626 0.03167248 0.2280928 0.02441759
## 0.27272727 0.03164589 0.2288865 0.02438971
## 0.28282828 0.03162197 0.2296235 0.02436467
## 0.29292929 0.03159971 0.2303388 0.02434211
## 0.30303030 0.03157874 0.2310489 0.02432155
## 0.31313131 0.03156173 0.2315992 0.02430552
## 0.32323232 0.03154803 0.2320180 0.02429228
## 0.33333333 0.03153681 0.2323416 0.02428132
## 0.34343434 0.03152951 0.2324942 0.02427372
## 0.35353535 0.03152481 0.2325401 0.02426774
## 0.36363636 0.03152236 0.2324904 0.02426348
## 0.37373737 0.03152211 0.2323449 0.02426146
## 0.38383838 0.03152373 0.2321187 0.02426054
## 0.39393939 0.03152655 0.2318482 0.02426129
## 0.40404040 0.03153109 0.2315051 0.02426338
## 0.41414141 0.03153657 0.2311284 0.02426600
## 0.42424242 0.03154252 0.2307384 0.02426923
## 0.43434343 0.03154915 0.2303231 0.02427274
## 0.44444444 0.03155575 0.2299191 0.02427619
## 0.45454545 0.03156261 0.2295110 0.02428055
## 0.46464646 0.03156938 0.2291177 0.02428478
## 0.47474747 0.03157655 0.2287130 0.02428915
## 0.48484848 0.03158419 0.2282948 0.02429406
## 0.49494949 0.03159214 0.2278679 0.02429935
## 0.50505051 0.03160022 0.2274395 0.02430454
## 0.51515152 0.03160838 0.2270130 0.02430972
## 0.52525253 0.03161673 0.2265826 0.02431516
## 0.53535354 0.03162544 0.2261422 0.02432109
## 0.54545455 0.03163421 0.2257061 0.02432718
## 0.55555556 0.03164303 0.2252739 0.02433359
## 0.56565657 0.03165185 0.2248479 0.02433995
## 0.57575758 0.03166047 0.2244389 0.02434604
## 0.58585859 0.03166897 0.2240418 0.02435201
## 0.59595960 0.03167783 0.2236318 0.02435877
## 0.60606061 0.03168665 0.2232287 0.02436558
## 0.61616162 0.03169524 0.2228425 0.02437256
## 0.62626263 0.03170373 0.2224664 0.02437973
## 0.63636364 0.03171237 0.2220869 0.02438675
## 0.64646465 0.03172090 0.2217179 0.02439337
## 0.65656566 0.03172960 0.2213448 0.02440022
## 0.66666667 0.03173850 0.2209657 0.02440728
## 0.67676768 0.03174776 0.2205740 0.02441468
## 0.68686869 0.03175738 0.2201696 0.02442237
## 0.69696970 0.03176727 0.2197579 0.02443044
## 0.70707071 0.03177724 0.2193468 0.02443851
## 0.71717172 0.03178721 0.2189406 0.02444673
## 0.72727273 0.03179733 0.2185309 0.02445492
## 0.73737374 0.03180750 0.2181248 0.02446299
## 0.74747475 0.03181800 0.2177068 0.02447151
## 0.75757576 0.03182867 0.2172855 0.02448023
## 0.76767677 0.03183944 0.2168640 0.02448931
## 0.77777778 0.03185028 0.2164444 0.02449824
## 0.78787879 0.03186125 0.2160230 0.02450726
## 0.79797980 0.03187255 0.2155911 0.02451662
## 0.80808081 0.03188388 0.2151621 0.02452598
## 0.81818182 0.03189517 0.2147387 0.02453549
## 0.82828283 0.03190667 0.2143104 0.02454516
## 0.83838384 0.03191846 0.2138737 0.02455492
## 0.84848485 0.03193037 0.2134360 0.02456487
## 0.85858586 0.03194244 0.2129950 0.02457484
## 0.86868687 0.03195474 0.2125477 0.02458488
## 0.87878788 0.03196720 0.2120981 0.02459502
## 0.88888889 0.03197983 0.2116460 0.02460522
## 0.89898990 0.03199247 0.2111971 0.02461529
## 0.90909091 0.03200512 0.2107518 0.02462530
## 0.91919192 0.03201799 0.2103014 0.02463541
## 0.92929293 0.03203093 0.2098519 0.02464548
## 0.93939394 0.03204413 0.2093953 0.02465563
## 0.94949495 0.03205769 0.2089269 0.02466596
## 0.95959596 0.03207129 0.2084610 0.02467622
## 0.96969697 0.03208469 0.2080081 0.02468639
## 0.97979798 0.03209823 0.2075528 0.02469684
## 0.98989899 0.03211186 0.2070981 0.02470744
## 1.00000000 0.03212568 0.2066400 0.02471817
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.3737374.
## fraction
## 38 0.3737374## Warning: Removed 1 rows containing missing values (geom_point).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] "Coefficients"
## x4 x7 x8 x9 x10 x11 x14 x16
## -2.069608e-03 6.898773e-03 6.397636e-04 3.630845e-03 8.986205e-04 4.087638e-04 -6.599386e-05 1.205132e-03
## x17 x21 stat3 stat4 stat5 stat13 stat14 stat23
## 1.269714e-03 7.579729e-04 2.541253e-05 -5.038086e-04 -1.957314e-04 -4.330076e-04 -1.027616e-03 4.749886e-04
## stat24 stat25 stat26 stat35 stat37 stat41 stat43 stat51
## -4.161709e-04 -2.362641e-04 -1.161015e-04 -1.488183e-04 -2.486764e-04 -5.396841e-04 -9.513741e-05 4.031533e-05
## stat54 stat59 stat60 stat91 stat92 stat98 stat100 stat103
## -1.131561e-04 3.152082e-04 1.421247e-04 -3.375154e-04 -1.854312e-05 5.556434e-03 6.976173e-04 -6.574468e-05
## stat104 stat106 stat110 stat114 stat121 stat131 stat144 stat146
## -1.522628e-04 -3.015687e-05 -5.025484e-03 2.331519e-05 -1.955973e-05 1.288268e-04 1.498213e-04 -2.514983e-04
## stat149 stat156 stat195 stat202 stat204 stat214 stat217 x18.sqrt
## -6.254883e-04 4.295890e-04 1.031131e-04 -5.003651e-05 -5.286024e-04 -6.567020e-05 3.240432e-04 1.139096e-02Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE, transformation = t)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2.048 2.084 2.097 2.096 2.109 2.141
## [1] "lars Test MSE: 0.00103767872694165"
Session Info
sessionInfo()## R version 3.5.2 (2018-12-20)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 14393)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252 LC_CTYPE=English_United States.1252 LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C LC_TIME=English_United States.1252
##
## attached base packages:
## [1] parallel stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] knitr_1.22 htmltools_0.3.6 reshape2_1.4.3 lars_1.2
## [5] doParallel_1.0.14 iterators_1.0.10 caret_6.0-81 leaps_3.0
## [9] ggforce_0.2.1 rlist_0.4.6.1 car_3.0-2 carData_3.0-2
## [13] bestNormalize_1.3.0 scales_1.0.0 onewaytests_2.0 caTools_1.17.1.2
## [17] mosaic_1.5.0 mosaicData_0.17.0 ggformula_0.9.1 ggstance_0.3.1
## [21] lattice_0.20-38 DT_0.5 ggiraphExtra_0.2.9 ggiraph_0.6.0
## [25] investr_1.4.0 glmnet_2.0-16 foreach_1.4.4 Matrix_1.2-15
## [29] MASS_7.3-51.1 PerformanceAnalytics_1.5.2 xts_0.11-2 zoo_1.8-4
## [33] forcats_0.4.0 stringr_1.4.0 dplyr_0.8.0.1 purrr_0.3.1
## [37] readr_1.3.1 tidyr_0.8.3 tibble_2.0.1 ggplot2_3.1.0
## [41] tidyverse_1.2.1 usdm_1.1-18 raster_2.8-19 sp_1.3-1
## [45] pacman_0.5.1
##
## loaded via a namespace (and not attached):
## [1] readxl_1.3.1 backports_1.1.3 plyr_1.8.4 lazyeval_0.2.1 splines_3.5.2 mycor_0.1.1
## [7] crosstalk_1.0.0 leaflet_2.0.2 digest_0.6.18 magrittr_1.5 mosaicCore_0.6.0 openxlsx_4.1.0
## [13] recipes_0.1.4 modelr_0.1.4 gower_0.2.0 colorspace_1.4-0 rvest_0.3.2 ggrepel_0.8.0
## [19] haven_2.1.0 xfun_0.5 crayon_1.3.4 jsonlite_1.6 survival_2.43-3 glue_1.3.1
## [25] polyclip_1.10-0 registry_0.5-1 gtable_0.2.0 ppcor_1.1 ipred_0.9-8 sjmisc_2.7.8
## [31] abind_1.4-5 rngtools_1.3.1 bibtex_0.4.2 Rcpp_1.0.0 xtable_1.8-3 foreign_0.8-71
## [37] stats4_3.5.2 lava_1.6.5 prodlim_2018.04.18 htmlwidgets_1.3 httr_1.4.0 RColorBrewer_1.1-2
## [43] pkgconfig_2.0.2 farver_1.1.0 nnet_7.3-12 labeling_0.3 tidyselect_0.2.5 rlang_0.3.1
## [49] later_0.8.0 munsell_0.5.0 cellranger_1.1.0 tools_3.5.2 cli_1.0.1 generics_0.0.2
## [55] moments_0.14 sjlabelled_1.0.17 broom_0.5.1 evaluate_0.13 ggdendro_0.1-20 yaml_2.2.0
## [61] ModelMetrics_1.2.2 zip_2.0.1 nlme_3.1-137 doRNG_1.7.1 mime_0.6 xml2_1.2.0
## [67] compiler_3.5.2 rstudioapi_0.9.0 curl_3.3 tweenr_1.0.1 stringi_1.4.3 highr_0.7
## [73] gdtools_0.1.7 pillar_1.3.1 data.table_1.12.0 bitops_1.0-6 insight_0.1.2 httpuv_1.4.5.1
## [79] R6_2.4.0 promises_1.0.1 gridExtra_2.3 rio_0.5.16 codetools_0.2-15 assertthat_0.2.0
## [85] pkgmaker_0.27 withr_2.1.2 nortest_1.0-4 mgcv_1.8-26 hms_0.4.2 quadprog_1.5-5
## [91] grid_3.5.2 rpart_4.1-13 timeDate_3043.102 class_7.3-14 rmarkdown_1.12 shiny_1.2.0
## [97] lubridate_1.7.4